4. Smaller cylinder: r = 3 in., h = 5 in. 6. Let 3x the measure of the first angle. Let x the measure of the second angle.

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1 Chapter : Linear Equations and Inequalities in One Variable.6 Check Points. A, b A bh h h h The height of the sail is ft.. Use the formulas for the area and circumference of a circle. The radius is 0 ft. A r A (0) 00 6 or 7 The area is 00 ft or approximately 6 ft or 7 ft. C r C (0) 0 6 The circumference is 0 ft or approximately 6 ft.. The radius of the large pizza is 9 inches, and the radius of the medium pizza is 7 inches. large pizza: Ar (9 in.) 8 in. in. medium pizza: Ar (7 in.) 9 in. in. For each pizza, find the price per inch by dividing the price by the area. Price per square inch for the large pizza $0.00 $0.00 $ in. in. in. Price per square inch for the medium pizza $.00 $.00 $ in. in. in. The large pizza is the better buy.. Smaller cylinder: r = in., h = in. V r h V () The volume of the smaller cylinder is in.. Larger cylinder: r = in., h = 0 in. V r h V () 0 90 The volume of the smaller cylinder is 90 in.. The ratio of the volumes of the two cylinders is V larger 90 in.. V smaller in. So, the volume of the larger cylinder is times the volume of the smaller cylinder.. Use the formula for the volume of a sphere. The radius is. in. V r V.. 8 The volume is approximately 8 in.. Thus the 0 cubic inches will not be enough to fill the ball. About more cubic inches are needed. 6. Let x the measure of the first angle. Let x the measure of the second angle. Let x 0 the measure of the third angle. x x( x0) x 0 x 0 x 0 0 The three angle measures are 0, 0, and 0. 7 Copyright 0 Pearson Education, Inc.

2 Introductory and Intermediate Algebra for College Students E Section.6 7. Step Let x = the measure of the angle. Step Let 90 x = the measure of its complement. Step The angle s measure is twice that of its complement, so the equation is x (90 x). Step Solve this equation x (90 x) x 80 x xx 80xx x 80 x 60 The measure of the angle is 60. Step The complement of the angle is , and 60 is indeed twice 0..6 Concept and Vocabulary Check.. A bh A r. C r. radius; diameter. V lwh 6. V r h complementary 9. supplementary x; 80 x.6 Exercise Set. Use the formulas for the perimeter and area of a rectangle. The length is ft and the width is ft. P lw P P 86 The perimeter is ft. A lw A The area is ft.. Use the formula for the area of a triangle. The base is 0 m and the height is m. A bh A 0 9 The area is 9 m. 6. Use the formula for the area of a trapezoid. The bases are 7 meters and 6 meters and the height is 8 meters. A hab A A The area is 67 m. 8. A 0; w A lw 0 l 70 l The length of the swimming pool is 70 ft. 0. A0, b 6 A bh 0 6h 60 6h 0 h The height is 0 ft. Copyright 0 Pearson Education, Inc. 7

3 Chapter : Linear Equations and Inequalities in One Variable. P 08, w 6 P lw 08 l 6 08 l 9 6 l 8 l The length of the rectangle is 8 cm.. Use the formula for the area and circumference of a circle. The radius is 9m. A r A 9 8 The area is 8 m or approximately m. C r C The circumference is 8 m or approximately 7 m. 6. Since the diameter is 0 ft, the radius is 0 0 ft. A r A The area is 00 ft or approximately 7 ft. C r C The circumference is 0 ft or approximately 6 ft. 8. C r 6 r 6 r 8 r The radius is 8 in. and the diameter is 8 6 in. 0. Use the formula for the volume of a rectangular solid. The length is cm and width and height are each cm. V lwh V The volume is cm.. Use the formula for the volume of a cylinder. The radius is 6 cm and the height is 8 cm. V r h V The volume is 88 cm or approximately 90 cm.. Use the formula for the volume of a sphere. The diameter is in., so the radius is in. V r V 0 78 The volume is 0 in or approximately 78 in. 6. Use the formula for the volume of a cone. The radius is m and the height is 6 m. V r h V The volume is 00 m or approximately 9 m. 7 Copyright 0 Pearson Education, Inc.

4 Introductory and Intermediate Algebra for College Students E Section.6 8. V r h V r h V r h V r h r r V V h or h r r 6. Let x = the measure of the smallest angle. Let x = the measure of the second angle. Let x + 0 = the measure of the third angle. xxx x 0 x 90 x 0 60 The three angle measures are 0, 90, and Smaller cylinder; r = in., h = in. V r h V V The volume of the smaller cylinder is in. Large cylinder: r = ( in.) = 8 in., h = in. V r h V 8 V 9 The volume of the larger cylinder is 9 in.. The ratio of the volumes of the two cylinders is VLarger 9 6, so the volume of the larger VSmaller cylinder is 6 times the volume of the smaller cylinder.. The sum of the measures of the three angles of a triangle is 80. xxx x 8 x 8 x 0 68 The three angle measures are 8, 8, and If the measure of an angle is, the measure of its complement is 90 = If the measure of an angle is, the measure of its complement is 90 = 88. If the measure of an angle is 9, the measure of its supplement is 80 9 = 87.. If the measure of an angle is 79., the measure of its supplement is = Step Let x = the measure of the angle. Step Then 90 x = the measure of its complement. Step The angle s measure is 78 less than that of its complement, so the equation is x 90 x 78. Step Solve this equation x 90 x78 x x x x 6 The measure of the angle is 6. Step The complement of the angle is 90-6 = 8, and 6 is 78 less than 8.. xx 80 0x 80 x 8 x 7 90 The three angle measures are 8, 7, and 90. Copyright 0 Pearson Education, Inc. 7

5 Chapter : Linear Equations and Inequalities in One Variable 8. Step Let x = the measure of the angle. Step Then 80 x = the measure of its supplement. Step The angle s measure is 6 more than three times that of its supplement, so the equation x 80 x 6. is Step Solve this equation x 80 x6 x 0 x6 x 6 x x 6 x 9 The measure of the angle is 9. Step The measure of its supplement is 80-9 =, and 9 = ( ) + 6, so the proposed solution checks. 0. Step Let x = the measure of the angle. Step Let 80 x = the measure of its supplement, and, 90 x = the measure of its complement. Step The measure of the angle s supplement is 0 more than three times that of its complement, so the equation is 80 x (90 x) 0. Step Solve this equation 80 x 90 x 80 x 80 x 80 x x 80 xx xx 80 x x The measure of the angle is. Step The measure of its supplement is 8 and the measure of its complement is 8. Since 8 = (8 ) +, the proposed solution checks.. Divide the shape into a triangle and a rectangle. 0 m m m m m 0 m m m entire figure rectangle triangle A A A Aentire figure lw bh The area of the figure is 00 m.. Subtract the area of the two smaller circles from the area of the larger circle. Note that the radius of the large circle is and note that the two smaller circles are the same size. A A A shaded larger circle smaller circle R r () () (6) () The shaded area is 8 cm. 6. Subtract the volume of the smaller cylinder from the volume of the larger cylinder. V V V shaded larger cylinder smaller cylinder R hr h The volume of the shaded region is 80 cubic inches. 76 Copyright 0 Pearson Education, Inc.

6 Introductory and Intermediate Algebra for College Students E Section.6 8. a. The area of the lot is 00 ft00 ft 00, 000 ft. The area of the house is 00 ft60 ft 6000 ft. The area of the shed is 0 ft0 ft 00 ft. The area of the driveway is 0 ft00 ft 000 ft. Therefore, the area of the lawn is 00, ,600 ft. Since each bag of fertilizer covers 000 square feet and 9, 600.9, bags of fertilizer 000 will be needed. b. The cost of the fertilizer is $ $ The radius of the large pizza is 6 inches = 8 inches, and the radius of each small pizza is 0 inches = inches. Large pizza: Ar 8 in. 6 in. 0 in. Small pizza: Ar in. in. 79 in. The area of one large pizza is about 0 in. and the area of two small pizzas is about (79 in. ) = 8 in.. Since the price of one large pizza is the same as the price of two small pizzas and the large pizza has the greater area, the large pizza is the better buy. (Because the prices are the same, it is not necessary to find the prices per square inch in this case.) 6. The area of the rectangular portion of the floor is (60 ft)(0 ft) = 00 ft. Since the radius of each semicircle is 0 ft and the two semicircles together make one circle, the area of the two semicircular portion of the floor is 0 ft 00 ft. Therefore, the area of the dance floor is 00 ft 00 ft. Since the flooring costs $0.00 per square foot, the cost of hardwood flooring for the dance floor will $ $6, 66. be about 6. The circumference of the garden is (0 ft) = 60 ft. Since 6 in. = ft., the number of plants needed is To the nearest whole number, 77 plants are needed. 66. The volume of the foundation is ( yd)( yd)( yd) = yd. Since each truck holds 6 yd of dirt, truckloads will be needed. Since the charge 6 to remove the dirt is $0 per load, the cost to have all the dirt hauled away is ($0) $ The volume of each tunnel is V r h V 0,000 V 00, 000 The volume of each tunnel is 00,000 m., so the volume of all three tunnels, which is the total amount of dirt that had to be removed, is 00, 000, 00, 000 m, 769, 900 m Answers will vary. 80. does not make sense; Explanations will vary. Sample explanation: The sum of the three angles of the triangle must be 80, but these three values total makes sense 8. true 86. true Copyright 0 Pearson Education, Inc. 77

7 Chapter : Linear Equations and Inequalities in One Variable 88. Consider the following diagram: 0 The area of the outer rectangle (pool plus path) is (6 ft)(0 ft) = 70 ft. The area of the inner rectangle (pool only) is (0 ft)( ft) = 0 ft. Therefore, the area of the walk is 70ft 0ft 00ft. Since the cost to resurface the path is $ per square foot, the total cost of resurfacing the path is 00($) = $ If the length, width, and height of a rectangular solid are each multiplied by 0, the volume will be multiplied by The volume of the car will be 000 times that of the model. 9. P sb for s Pb s P b s Pb Pb s or s x x 9. 7 Multiply both sides by the LCD,. x x 7 x8 x8x x x 8 x 888 x x x 8 8. The solution set is x 8 8 8, true is a solution to the inequality. 96. y 7 (6) 7 7 7, true 6 is a solution to the inequality. 97. ( x) 8( x) x6 8x8 7x68x8 7x8x68x8x8 x 6686 x x The solution set is..7 Check Points. a. b. c.. a. 0, b., 78 Copyright 0 Pearson Education, Inc.

8 Introductory and Intermediate Algebra for College Students E Section.7. x 69 x 6696 x The solution set is, or xx.. 8x7x 8x7x7x7x x x x The solution set is,. a. or xx. x x x 8 The solution set is,8 or xx 8. b. 6x 8 6x x The solution set is 6. y 7 y 7 y 0 y 0 y The solution set is, or xx, or yy x 6x 68x 668x 6 8x 8 8x x The solution set is 8. ( x) ( x) x6x6 x7x8 xx7xx8 x 7 8 x x x x The solution set is 9. ( x) x x8 x xx8 xx 8, false There is no solution or., or xx., or xx. 0. ( x) x x xx xxxx, true The solution is, or xx is a real number. Copyright 0 Pearson Education, Inc. 79

9 Chapter : Linear Equations and Inequalities in One Variable. Let x your grade on the final examination x x 80 x 80 x 80 x 00 x 00 x 66 x 8 To earn a B you must get at least 8% on the final examination.. Let x the number of people you invite to the picnic x To can invite at most people to the picnic. 6. x 6 8. x x 6. x 0., 6. 7, 8.,.7 Concept and Vocabulary Check 0.,. (,). (, ). b c. bc. bc 6. subtracting ; dividing; ; direction; >; <. x 6 x,. x x 7 7, 7. or the empty set 8. (, ).7 Exercise Set 6. y 0 y,. x. x 0 80 Copyright 0 Pearson Education, Inc.

10 Introductory and Intermediate Algebra for College Students E Section.7 8. x9 x xx 9 x 7, y y 0 7 y, 0. x8 x xx8 x 9,9. 8x97x 8x7x 9 x 6. 6, x 6 x 6 7 x 6 7, x x x 6 6, x x x,. 6x 8 6x x, 6. y y 9 y y, 6. 7x 6 7x x 8 8, 8. 7x 7x 7 7 x, Copyright 0 Pearson Education, Inc. 8

11 Chapter : Linear Equations and Inequalities in One Variable 0. 7x 7x 7 7 x,. 0x 0 0x x 7,7. 6. y y y, x x, x 8. x x x x x, 60. 8x 8x 8x 6 8x x, x x x, 6. x x x 9 x 9 x 66., x x x 6 6 x 6,6 x 8 Copyright 0 Pearson Education, Inc.

12 Introductory and Intermediate Algebra for College Students E Section x x6 6xx x6x x 6 x 6 x 8, x 8 x 76. 7yy 7y80y y 0y y 00y 8y 0 y, 70. y79y y79y 9y9y y 7 y 77 7 y y y, 7. y 8y 8y 8y 6 8y y, 7. x x6 xx6 x6x6 x6x x6x x 66 x 6666 x 0 0, x 78. x x x x , x x x x x 8 8, 8. x x6 xx6x 6 The original inequality is equivalent to the false statement 6, so the inequality has no solution. The solution set is. Copyright 0 Pearson Education, Inc. 8

13 Chapter : Linear Equations and Inequalities in One Variable 8. x x0 xx x0x 0 The original inequality is equivalent to the true statement 0 The solution is the set of all real numbers, written xx is a real number or,. 9. y mxb yb mxbb yb mx y b mx m m yb yb x or x m m 86. xx xx6 xx x6x 6 Since 6 is a false statement, the original inequality has no solution. The solution set is. 88. x Since 0 0 is a true statement, the original inequality is true for all real numbers. The solution set is xx is a real number or, xx 6xx 6xx 6x x x 0 6xx xx x 0,0 9. xab xaa ba xba x ba b a x 96. x is between and, so x. 98. x is greater than or less than, so x. 00. weird 0. supersede, inoculate 0. cemetery, accommodation, harass 06. S. S is no more than 0 billion S x 8 According to the model, there will be no more than 0 billion stamped letters mailed in the U.S. 8 years after 000. In other words from 08 onward. 08. a. If you get 00 on the final, your average will be Since and it is not possible to get more than 00 on the final, an A in the course is not possible. b. Let x = your grade on the final exam x x x 0 x 0 x 0 x 68 You must get at least 68 to get a B in the course. 8 Copyright 0 Pearson Education, Inc.

14 Introductory and Intermediate Algebra for College Students E Section.7 0. Let x = the number of miles driven x x x 080 You can drive up to 080 miles.. Let x = the number of cement bags x 9 Up to 9 bags of cement can safely be lifted on the elevator in one trip.. 6. Answers will vary. 8. makes sense 0. makes sense. false; Changes to make the statement true will vary. A sample change is: The statement x is at most is written x.. true 6. Let x = the number of hours a person works out at the fitness club yearly. Yearly cost at first club (in dollars) 00 x 00 x Yearly cost at second club 0.7 The first club will be cheaper if 00 x 0.7 Solve this inequality. 00 x x 80 The first club will be cheaper if the person works out more than 80 hours a year y.8y y.8y.8y..8y 6.8.y. 6.8.y y 9..y 9... y 6. 6., 9. A = PB, A = 8, P = 0% = 0. A PB 8 0.B 8 0.B B 8 is 0% of Let x the width of the rectangle. Let x the length of the rectangle. P l w ( x) x x0 x x 0 0 x 0 0 x 6 x x 6 x The width is 6 inches and the length is inches.. 6x8 6x 6x xx x 6 x 66 6 x 8 x 8 x Check: , true The solution is set is. Copyright 0 Pearson Education, Inc. 8

15 Chapter : Linear Equations and Inequalities in One Variable. xy ( ), true Yes, the values make it a true statement.. xy () 8, false No, the values make it a false statement.. y x y ( 6) y y Chapter Review Exercises. x 0 x x The solution is set is.. y 8 8 y 8 8 y The solution is set is.. 7z6z9 7z6z 6z96z z 9 z 9 z The solution is set is.. x x0 xx0 xx x0x x 0 x 0 x The solution is set is.. 6xx9 7x x8x x8x xx x 8 x 88 8 x The solution is set is. x 0 8 x x 80 The solution is set is 80. y 7 8 y y 6 The solution is set is z 77 7z z The solution is set is y 6 9y 9 9 y The solution is set is. 86 Copyright 0 Pearson Education, Inc.

16 Introductory and Intermediate Algebra for College Students E Chapter Review 0... x 9 9 x x x The solution is set is. 0 y 0 y y The solution is set is. x x x The solution is set is. 6. z0z z0z zz z 00 z 0000 z 0 z 0 z 0 The solution is set is x x x x x x 8 x 8 x The solution is set is.. x 0 x x 0 x 0 x 0 The solution is set is 0.. x 9 x 999 x x x 6 The solution is set is 6.. y y y y y The solution is set is. 8. x 98x x8x 98x8x 6x 9 6x 9 6x 6 6x x. The solution is set is 9. a. 009 is years after 00. P.n P.() 6 According to the formula, 6% of returns are filed electronically. The formula underestimates the actual value given in the bar graph by %. b. P.n 9.n.n.n.. n If trends continue, 9% of returns will be filed electronically years after 00, or 07. Copyright 0 Pearson Education, Inc. 87

17 Chapter : Linear Equations and Inequalities in One Variable 0. 97x6 x8 x x8 x x8x x 8 x 8 x x x The solution is set is.. x x x x x x x x The solution is set is.. y 6 y y y yy yy yy y y y y The solution is set is.. x8x x 7 x 7x xx x 7 x 77 7 x 9 x 9 x The solution is set is.. yy6y. 6. y8y6y y06y y06y 6y6y 0 y 0 0 y y 0 The solution is set is 0. x x 6 To clear fractions, multiply both sides by the LCD, which is 6. x x x x x x6 x x x6x x 6 x 6 x. The solution is set is x x 0 Multiply both sides by the LCD, which is 0. x x x x x x x x x x 6 x 6 x The solution is set is. 88 Copyright 0 Pearson Education, Inc.

18 Introductory and Intermediate Algebra for College Students E Chapter Review 7. Multiply both sides by 00 to clear the decimals (0. 8.7) 00(.) 0x 87 0x 0 x 9 The solution set is First apply the distributive property to remove the parentheses, and then multiply both sides by 00 to clear the decimals. 0.( x).0. 0.x (0.x0.) 00(. 0. x) 0x0 0 0x x The solution set is x6 x x 0 x x x 0 xx 0 Since = 0 is a false statement, the original equation is inconsistent and has no solution or. 0. x 8x8 8x8x8 8x88x8 8x88x 8x88x 8 8 Since 8 = 8 is a true statement, the solution is the set of all real numbers, written xx is a real number.. H a a 0.7a 0.7a 0.7a a If the optimal heart rate is beats per minute, the person is 0 years old.. I = Pr for r I Pr P P I I r or r P P. V Bh for h V Bh V Bh V Bh B B V V h or h B B. P l w for w Pl lwl Pl w P l w Pl Pl w or w B C. A for B B C A A BC AC BCC A C B or B AC Copyright 0 Pearson Education, Inc. 89

19 Chapter : Linear Equations and Inequalities in One Variable 6. T D pm for m T D D pmd T D pm T D pm p p T D T D m or m p p 7. A PB; P 8% 0.08, B 0 A A 9.6 8% of 0 is A PB; A90, P % B 90 0.B B 90 is % of A PB; A6, B 7 6 P 7 6 P P 6 is 8% of Increase = Percent Original First, find the increase: 6 = 6 6 P 6 6 P P The percent increase is 00%.. Decrease = Percent Original First, find the decrease: = P P 0. P The percent decrease is 0%.. Increase = Percent Original First, find the increase: 0 = P 0 P P The percent increase is.%.. Investment dollars lost last year were 0.0 $0, 000 $000. This means that $0,000 $000 = $9000 remains. Investment dollars gained this year are 0.0 $9000 $900. This means that $ $900 = $9900 of the original investment remains. This is an overall loss of $00. decrease = percent original 00 P 0, P 0, 000 0, 000 0, P The statement is not true. Instead of recouping losses, there is an overall % decrease in the portfolio.. a. h r 7 h 7r r h or h 7r b. h 7; r r 9 h 7(9) 6 The woman s height is 6 inches or feet, inches.. A PB 9 0.6B B B The average U.S. household uses 0 gallons of water per day. 6. Let x = the unknown number. 6x0 x 6x0x xx x 00 x 0000 x 0 x 0 The number is Copyright 0 Pearson Education, Inc.

20 Introductory and Intermediate Algebra for College Students E Chapter Review 7. Let x Buffett s net worth. Let x 9 Gate s net worth. x( x9) 99 xx999 x 999 x 90 x x 9 In 00 Buffett s net worth was $ billion and Gate s net worth was $ billion. 8. Let x the smaller page number. Let x the larger page number. xx9 x 9 x 9 x 6 The page numbers are 6 and Let x the percentage of females. Let x the percentage of males. x( x) 00 x x 00 x 00 x 00 x 98 x 9 x For Americans under 0, 9% are female and % are male. 0. Let x number of years after x 90 x 88 x 88 x According to this model, the U.S. defense budget will reach $90 billion in years after 00, or 0.. Let x the number of checks written x 8 You wrote 8 checks that month.. Let x the width of the field. Let x the length of the field. P l w 00 x x 00 6xx 00 8x 00 8x x x 0 x 0 The field is 0 yards wide and 0 yards long.. Let x the original price of the table. x x 0 The table s price before the reduction was $0.. Find the area of a rectangle with length 6. ft and width ft. Alw(6.)(). The area is. ft.. Find the area of a triangle with base 0 cm and height cm. A bh (0)() 0 The area is 0 cm. 6. Find the area of a trapezoid with bases yd and yd and height 0 yd. A h ( ab ) (0)( ) 0 7 The area is yd. Copyright 0 Pearson Education, Inc. 9

21 Chapter : Linear Equations and Inequalities in One Variable 7. Notice that the height of the middle rectangle is 6 0 m. 6. First, find the area of a trapezoid with bases 80 ft and 00 ft and height 60 ft. A h ( ab ) (60)(80 00) 00 The area of the yard is 00 ft. The cost is $0.(00) = $ The radius of the medium pizza is Using A lw we must find the sum of areas of the middle rectangle and the two side rectangles. A (0)(7) (6)(6) The area is 7608 m. 8. Since the diameter is 0 m, the radius is 0 0 m. C (0) 0 6 Ar (0) 00 The circumference is 0 m or approximately 6 m; the area is 00 m or approximately m. 9. A, b A bh h 7h 6 h The height of the sail is 6 ft. 60. Area of floor: Abh (ft)(ft) 80ft Area of base of stove: Abh ( ft)( ft) ft Area of bottom of refrigerator: Abh ( ft)( ft) ft The area to be covered with floor tile is 80 ft ft ft 6 ft. inches 7 inches, and the radius of each small pizza is 8 inches inches. Medium pizza: Ar (7 in.) 9 in. in. Small pizza: Ar (in.) 6 in. 0 in. The area of one medium pizza is approximately in. and the area of two small pizzas is approximately (0) 00 in.. Since the price of one medium pizza is the same as the price of two small pizzas and the medium pizza has the greater area, the medium pizza is the better buy. (Because the prices are the same, it is not necessary to find price per square inch in this case.) 6. Find the volume of a rectangular solid with length cm, width cm, and height cm. Alwh 60 The volume is 60 cm. 6. Find the volume of a cylinder with radius yd and height 8 yd. V r h () The volume is 8 yd 0 yd. 6. Find the volume of a sphere with radius 6 m. V r (6) The volume is 88 m 90 m. 9 Copyright 0 Pearson Education, Inc.

22 Introductory and Intermediate Algebra for College Students E Chapter Review 66. Find the volume of each box. V lwh(8m)(m)(m) 96m The space required for 0 containers is 0(96 m ) 800 m. 67. Since the diameter of the fish tank is 6 ft, the radius is ft. V r h () The volume of the tank is approximately 8 ft. Divide by to determine how many fish can be put in the tank There is enough water in the tank for 6 fish. Round down to 6, since 0.96 of a fish cannot be purchased. 68. The sum of the measures of the angles of any triangle is 80, so xxx 80. xxx 80 6x 80 x 0 If x = 0, then x = 90 and x = 60, so the angles measure 0, 60, and Let x = the measure of the second angle. Let x + = the measure of the first angle. Let x + = the measure of the third angle. x(x) ( x) 80 x 0 80 x 0 x If x =, then x + = () + = 8 and x + = + = 60. The angles measure 8,, and Let x = the measure of the angle. Let 80 x = the measure of its supplement. 80 x x 80 x If x =, then 80 x =. The measure of the angle is and the measure of its supplement is. 7. x 7. x 76., 77.,0 78. x x x 8 x 8 x, 70. If the measure of an angle is 7, the measure of its complement is If the measure of an angle is 7, the measure of its supplement is Let x = the measure of the angle. Let 90 x = the measure of its complement. x (90 x) x x x x 7. The measure of the angle is x x x 8 8, Copyright 0 Pearson Education, Inc. 9

23 Chapter : Linear Equations and Inequalities in One Variable x, 8. x6 x6 x 60 x 6606 x 6 6 x 6 6, x 8. 6x0x 6x0x6 6x0x x6x x 06 x 0060 x 6 x 6 x, 8. x x7 x x6x x 0x x 0xx x x 9x 9x 9x 8 9x x, 8. x x 6 x8 x86 x8 x x8x xx 8 Since 8 > is a true statement, the original inequality is true for all real numbers, and the solution set is xx is a real number. 8. x x x8 x x8x xx 8 Since 8 is a false statement, the original inequality has no solution. The solution set is. 86. Let x = the student s score on the third test. 7 x 60 7 x 60 7 x 80 6 x 80 6 x x 6 The student must score at least 6 on the third test to pass the course. 87. Let x the number of people you invite to the picnic x 0 You can invite at most 0 people to the party. 9 Copyright 0 Pearson Education, Inc.

24 Introductory and Intermediate Algebra for College Students E Chapter Test Chapter Test. x x x 8 x x 9 The solution set is.. x 7x x 7x 7x7x x The solution set is.. x 8 x x6 8 x6 8 x x6 x 8 6x 6 8 6x x 8 6x x 6 The solution set is.. y9y. 6. 6y9y 6y6y 6yy 6yy 9y 6 9y 6 9y 8 9y y The solution set is. x x x 0 The solution set is 0. x x 0 Multiply both sides by the LCD, 0. x x x x x06x x06x 6x6x x 0 x 000 x x x The solution set is. Copyright 0 Pearson Education, Inc. 9

25 Chapter : Linear Equations and Inequalities in One Variable 7. 9.x80..x 9.6 To clear the equation of decimals, multiply both sides by 0. 0(9.x80.) 0(.x9.6) 9x80 x96 9x x60 x 60 x 60 x The solution set is. 8. N.x80; N.x 80.x x.x.. x 60 The US population is expected to reach million 60 years after 960, in the year V r h for h V r h r r V V h or h r r P w l for w P w l l Pw lp PwP lp w lp w lp Pl w or w. A PB; P 6% 0.06, B 0 A A 8. 6% of 0 is 8... A PB; A=0, P 80% B B B 0 is 80% of 0.. A PB; A, B 0 P 0 P P is % of 0.. Let x = the unknown number x 6 The number is 6.. Let x the average number of vacation days for Americans. Let x 9 the average number of vacation days for Italians. x( x9) xx9 x 9 x 6 x x 9 Americans average vacation days and Italians average vacation days. 6. Let x = number of monthly calling minutes x 0.0 x 600 You can talk for 600 minutes. 96 Copyright 0 Pearson Education, Inc.

26 Introductory and Intermediate Algebra for College Students E Chapter Test 7. Let x = the width of the field. Let x the length of the field. P l w 0 x x 0 xx 0 6x 0 6x x x 7 x 0 The field is 7 yards wide and 0 yards long. 8. Let x = the book s original price. x0.0x x 8 8 x 0.80 x The price of the book before the reduction was $. 9. Find the area of a triangle with base 7 meters and height meters. A bh 7 7 The area of the triangle is 7 m. 0. Find the area of a trapezoid with height in, lower base 0 in and upper base 0 in. A h ( ab ) ()(0 0) 70 The area is in.. Notice that the height of the side rectangle is 69ft. Using A lw we must find the sum of areas of the upper rectangle and the side rectangle. A ()() ()(9) The area is 66 ft.. Find the volume of a rectangular solid with length in, width in, and height in. V lwh 8 The volume is 8 in.. Find the volume of a cylinder with radius cm and height 7 cm. V r h () The volume is 7 cm or approximately 0 cm.. The area of the floor is A (0ft)(0ft) 000ft. The area of each tile is A ( ft)( ft) ft. 000 ft The number of tiles needed is 00. ft Since there are 0 tiles in a package, the number of packages needed is Since each package costs $, the cost for enough tiles to cover the floor is 0($) $60.. A6, b 8 A bh 6 8h 6 h h The height of the sail is feet. 6. Let x = the measure of the second angle. Let x = the measure of the first angle. Let x 0 = the measure of the third angle. x x( x0) x x 6 x 0 The measure of the first angle is 6. The measure of the second angle is. The measure of the third angle is. Copyright 0 Pearson Education, Inc. 97

27 Chapter : Linear Equations and Inequalities in One Variable 7. Let x = the measure of the angle. Let 90 x = the measure of its complement. x (90 x) 6 x 06 x x 06 x The measure of the angle is. 8., 9., 0. x x x 6, 6. 69x 69x 66 9x 7 9x x,. xx6 xx xx xx x x x 7 7,. Let x = the student s score on the fourth exam x x x 0 8 x 0 x 9 The student must score at least 9 on the fourth exam to have an average of at least 80.. Let x = the width of the rectangle. (0) x 6 0 x x 6 0 x 6 x 8 The perimeter is greater than 6 inches when the width is greater than 8 inches. Cumulative Review Exercises (Chapters -) xx7 x 0x 0 0 0x The rational numbers are,, 0,, and ( x ) x 7. 0,000 < since 0,000 is to the left of on the number line. 8. 6(x y) 6( x) 6() 6( y) x6 0y 98 Copyright 0 Pearson Education, Inc.

28 Introductory and Intermediate Algebra for College Students E Cumulative Review 9. A0.9n69 A 0.9(0) 69 A 8 69 A According to the formula, % of seniors used alcohol in 000. This overestimates the actual value shown in the bar graph by %. 0. A0.9n69 0.9n n 6 0.9n n If trends continue, % of seniors will use alcohol 0 years after 980, or ( x) x 6x x 76x x 76xx x x 77x 77x 7 7 7x 7 7x x. The solution set is x x. Multiply both sides by the LCD,. x x x x x0 x0x x 0 x 0 x x The solution set is.. V Ah for A V Ah V Ah V Ah V Ah h h V V A or A h h. A = PB; A = 8, P = 0% = B 8 0.0B B 8 is 0% of 60.. Let x = the width of the parking lot. Let x 0 the length of the parking lot. P l w 00 (x0) x 00 x0 x 00 6x x x 0 6x x x 70 x 0 0 The parking lot is 70 yards wide and 0 yards long. 6. Let x = number of gallons of gasoline. 0.0x 0, x 0, x 7, 000 7,000 gallons of gasoline must be sold. 7., Copyright 0 Pearson Education, Inc. 99

29 Chapter : Linear Equations and Inequalities in One Variable 8. x x x 9 x 9 x, 9. ( x) (x) 6x x0 xx xx xx x x x x x 6 6, 0. Let x value of medical supplies sold x x x x x 7, 00 You must sell more than $7,00 worth of medical supplies. 00 Copyright 0 Pearson Education, Inc.