Practice Set 1.1 Algebraic Expressions and Real Numbers Translate each English phrase into an algebraic expression. Let x represent the number. 1. A number decreased by seven. 1.. Eighteen more than a number... Five times a number increased by four.. 4. Six less than the quotient of a number and five. 4. 5. The difference of nine and three times a number. 5. 6. Twice the sum of a number and twelve. 6. Evaluate each algebraic expression for the given values of the variables. 7. 6x 14 if x = 4 7. 8. 1 x if x = 8. 9. x x if x = 9. 10. x y if x = 5 and y = 4 10. 11. x + xy y if x = and y = 11. Determine whether the inequality is true of false. If it is false, rewrite it so that it is true. 1. 8 > 4 1. 1. 7 > 4 8 1. 14. 4.6 <.1 14. 15. 0 < 5. 15. 1
Use the given set to answer the following questions. { 18, 0.4, 1 1 5, 6, 5.8, 9, 0, 0.,, 7.6,, 10} 8 5 16. Name the integers. 16. 17. Name the rational numbers. 17. Use the given set to answer the following questions. π 4 15 {,, 8., 6 7 16 0, 5,, 10,, 1, π, 0. 6, 17.} 18. Name the irrational numbers. 18. 19. Name the natural numbers. 19. Determine whether each statement is true of false. 0. Every whole number is an integer. 0. 1. Some rational numbers are irrational. 1.. All natural numbers are rational numbers... Zero is a natural number.. 4. Irrational numbers are not real numbers. 4. 5. Whole numbers are positive and negative integers. 5.
Practice Set 1. Operations with Real Numbers and Simplifying Algebraic Expressions Fill in the blanks. 1. Absolute value is always.. When two negative numbers are added, the sum will be.. Reciprocals always have the because the product of reciprocals is positive. 4. The product of a negative number and a negative number is. 5. Division by zero is. 6. The quotient of a negative number and a positive number is. Add, subtract, multiply or divide. 7. 18 ( 1) 7. 8. 16 ( 4) 8. 9. 15 5 9. 10..7.4 10. 11. 6 ( )(0)( )(4) 11. 1. 5 5 8 6 1.
Simplify each algebraic expression using the order of operations. 1. 10 5(6 4 + 5) 1. 14. 5 + 8 4 + 4 + 10 + 14. 15. 14x (x 6) 10 15. 16. 18 7 16. 17. (10x 15 + x) (5x 4 + x) 17. 18. 16 4[18 (4 14 )] 18. 19. Use the commutative property of addition to write 19. an equivalent express to x + 18. 0. Use the distributive property to write an equivalent 0. expression to 6(x 4). 4
Practice Set 1. Graphing Equations Match each equation with its corresponding graph. 1. y = x + 4. y = x 1. y = x 4. y = x + 5. y = x 6. y = 1 x 4 7. y = x + 8. y = x 1 9. y = x +1 10. y = x a. b. c. d. e. f. g. h. i. j. 5
Graph each equation. 11. y = x 1. y = x 1. y = x +1 14. y = x 1 15. y = x+ 16. y = x 1 17. y = x 18. y = x 6
Answer the question with yes or no. Practice Set 1.4 Solving Linear Equations 1. Is 8 a solution to the equation 4x + 0 = x 16? 1.. Is 4 a solution to the equation 18 x + 0 = (5x 10)?. (a.) Solve each equation. (b.) Then state whether the equation is an identity, a conditional equation, or an inconsistent equation.. 5 ( x ) = 15 a. 4. 5 + (4x 4) = (x 1) 4a. 5. 1 1 5 y = y 5a. 8 8 8 _ 6. 5 (a 1) + 1 = a 4 + 8a 6a. 7. 6 (5y 1) + 4y = 0 7a. 8 + x x 5 8. = + 5 8a. 9. 0 = 8 5(x ) + 4x 9a. 10. 4(a + 1) + 6 = 5 + (6a 5) 10a. 7
11. 0.04x 0.06( x ) = 0. 16x 11a. 1. x 4 + 1 = x 6 15 1a. 1. 5( y ) (y + ) = 5y 4 1a. 14. x 1 x x + 8 = 5 4 10 14a. 15. 6 x ( x + 4) = x + ( x + 6) 15a. 16. 1 x + 8 = 10 x 16a. 17. 5 4(x ) = 1x 17a. x 1 x 18. = + 1 5 15 18a. 19. 4x 7 = 4(x ) + 5 19a. 0. 8.1x.7 =.4x + 0a. 8
Practice Set 1.5 Problem Solving and Using Formulas Choose the correct equation for each word problem. 1. One number exceeds another by 1. The sum of the numbers is 19. a. x +1 = 19 b. x + ( x + 1) = 19 c. x = x +1 + 19. When four times the sum of a number and is increased by 8, the result is 4. a. x + (4) + 8 = 4 b. 4 x + = 8 + 4 c. 4 ( x + ) + 8 = 4. When 0% of a number is added to the number, the result is 0. a. 0.0x = 0 b. x + 0 x = 0 c. x + 0.0x = 0 4. The second angle in a triangle is ten degrees more then the first and the third angle is twice the first increased by ten degrees. The sum of the degrees of any triangle is 180. a. x = 180 b. ( x ) + ( x + 10) + (x) = 180 c. x + ( x + 10) + (x + 10) = 180 5. After a 0% reduction, you purchase a watch for $88.What was the original cost of the watch? a. x 0.0x = 88 b. x 0 = 88 c. x 0.0 = 88 6. Including an 1% sales tax, a hotel charges $10.80 per night. Find the hotel s nightly charge before the tax was added. a. x + 0.1x = 10.80 b. x + 0.1 = 10. 80 c. x + 1 x = 10. 80 7. The length of the vacant lot is three times as long as the width. If the perimeter is 15 ft., find the measurements of the lot. a. x + x = 15 b. x ( x) = 15 c. x + (x) = 15 8. This month s cell phone bill is $45.00 The base charge is $0 per month with each minute costing 5. Find how many minutes where used this month. a. 0 +.05 = 45 b. 0 + 0.05x = 45 c. 0 x +.05x = 45 9
Write an equation for each situation. Then solve. 9. One number is five times another. Their sum is 7. Find the numbers. 10. Twice the sum of a number and eight is thirty-six. Find the number. 11. The length of a rectangle is four times the width. The perimeter of the rectangle is 55 inches. Find the dimensions of the rectangle. 1. When a number is increased by 8% of itself, the result is 54. Find the number. 1. The monthly cell phone bill is $85 which includes taxes, surcharges and 00 text messages. Any text messages after 00 cost $0.10 each. If the bill for one month is $107, find the total number of text messages. 14. The price of a new refrigerator is $195. If the store is having a 0% off sale, find the sale price of the refrigerator. Solve each formula for the specified variable. 15. d = rt for t 16. P = a + b + c for c 1 17. V = Br for B 9 18. F = C + for C 5 19. A n 60 r = π for n 1 0. A = h( B + b) for B 10
Practice Set 1.6 Properties of Integral Exponents Use the exponent rules to simplify each expression. 6 1. y y 1. 4 7. a a a. 4 5. (6x y )(1x y ). 5 4 4. ( 8xy )(x y) 4. 5. 4 5. 6. 5 6. 4 7. ( 4x y ) 7. 8. ( 5x y) 8. 9. 5x 5x 6 y y 5 9. 4 0x y 10. 4 6 10x y 10. 11
0 1 0 11. x + 11. 0 0 0 0 1. 5 + 5x (5x) + x 1. 4 1. ( ) 1. 14. (5x) 14. 4 (x y ) 15. 4 (9x y) 15. 5 (x y ) 16. 5 (x y ) 16. 5 18m n 17. 8 m n 17. 4 4a b c 18. 4 4a b c 8 18. 4 19. (4x y )( x y ) 19. 5 6 (6x y)(x y ) 0. 6 7 ( x y )(xy ) 0. 1
Practice Set 1.7 Scientific Notation Rewrite each number in scientific notation. 1. 58,000 1.. 9,000,000.. 0.00004. 4. 0.000008 4. 5. 8,0,000 5. Rewrite each number in decimal notation. 4 6. 6.7 10 6. 5 7..9 10 7. 7 8. 8 10 8. 6 9. 1.4 10 9. 10. 5.4 10 10. 1
Perform the indicated operations. Give answers in scientific notation. 9 4 11. (.6 10 )( 10 ) 11. 5.4 10 1. 6 10 5 8.4 10 1..1 10 4 1. 1. 14. 5 (6. 10 )(.1 10 ) 14. 15. 6 (1.7 10 )(5.8 10 ) 15. 7. 10 16. 4 8 10 1 16. Rewrite each number in scientific notation. Then perform the indicated operation and give the answer in scientific notation. 17. (8,000,000)(0.000) 17. 18. 0.000005 0.00000001 18. 19. 4,00,000,000 0.000016 19. 0. (0.000008)(0.00000045) 0. 14