Study Guide and Intervention

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1 NAME DATE PERIOD Study Guide and Intervention Algebra: Equations An equation is a sentence in mathematics that contains an equals sign. The solution of an equation is the value that when substituted for the variable makes the equation true. Solve 23 y 29 mentally. Lesson y 29 Write the equation You know that 23 6 is Simplify. The solution is 6. What value of x is a solution of x 8 26? A. 16 B. 17 C. 18 D. 19 Substitute each value for x to determine which makes the left side of the equation equivalent to the right side. Replace x with 16. Replace x with 17. Replace x with 18. x 8 26 x 8 26 x false false true The value of 18 makes the equation true. So, the answer is C. Solve each equation mentally. 1. k g y a x r h 8. n x 10. h y f 90 Name the number that is the solution of the given equation h 10; 7, 17, n 11 4; 44, 55, 66 Glencoe/McGraw-Hill 21 Mathematics: Applications and Concepts, Course 2

2 NAME DATE PERIOD Study Guide and Intervention Solving Addition and Subtraction Equations Remember, equations must always remain balanced. If you subtract the same number from each side of an equation, the two sides remain equal. Also, if you add the same number to each side of an equation, the two sides remain equal. Solve x Check your solution. x 5 11 Write the equation. 5 5 Subtract 5 from each side. x 6 Simplify. Check x 5 11 Write the equation Replace x with This sentence is true. The solution is t 12 Write the equation Add 12 to each side. 27 t Simplify. Solve 15 t 12. Check your solution. Check 15 t 12 Write the equation Replace t with This sentence is true. The solution is 27. Solve each equation. Check your solution. 1. h m p y 8 5. w k r z b c j v w y f n 12 Glencoe/McGraw-Hill 190 Mathematics: Applications and Concepts, Course 2

3 NAME DATE PERIOD Study Guide and Intervention Solving Multiplication Equations If each side of an equation is multiplied by the same number, the resulting equation is equivalent to the given one. You can use this property to solve equations involving multiplication and division. Solve 45 5x. Check your solution. 45 5x Write the equation x 5 5 Divide each side of the equation by 5. 9 x Check 45 5x Write the original equation. 45 5(9) Replace x with 9. Is this sentence true? The solution is y Write the equation y 3 Divide each side by 3. 7 y 21 ( 3) 7 Check 21 3y 21 3(7) The solution is 7. Solve 21 3y. Check your solution. Write the original equation. Replace y with 7. Is this sentence true? Solve each equation. Then check your solution. 1. 8q p m h 5. 6n x y b Lesson a m t r 13. 3a h k z Glencoe/McGraw-Hill 195 Mathematics: Applications and Concepts, Course 2

4 NAME DATE PERIOD Study Guide and Intervention Solving Two-Step Equations To solve two-step equations, you need to add or subtract first. Then divide to solve the equation. 7v 3 25 Write the equation. 3 3 Add 3 to each side. 7v 28 Simplify. 7 v Divide each side by 7. v 4 Solve 7v Check your solution. Simplify. Check 7v 3 25 Write the original equation. 7(4) 3 25 Replace v with Multiply The solution checks. The solution is 4. Solve x. Check your solution x Write the equation. 8 8 Subtract 8 from each side. 18 3x Simplify. 18 3x 3 3 Divide each side by 3. 6 x Simplify. Check x ( 6) 10 8 ( 18) The solution is 6. Write the original equation. Replace x with 6. Multiply. The solution checks. Solve each equation. Check your solution. 1. 4y x k n c p t r n b p y t x z g x q c y Glencoe/McGraw-Hill 200 Mathematics: Applications and Concepts, Course 2

5 NAME DATE PERIOD Study Guide and Intervention Algebra: Solving Equations Multiplicative inverses, or reciprocals, are two numbers whose product is 1. To solve an equation in which the coefficient is a fraction, multiply each side of the equation by the reciprocal of the coefficient. Find the multiplicative inverse of Rename the mixed number as an improper fraction Multiply by to get the product The multiplicative inverse of is Lesson 6 5 Solve 4 x 8. Check your solution. 5 4 x x x 10 The solution is 10. Write the equation. Multiply each side by the reciprocal of 4 5, 5 4. Simplify. Find the multiplicative inverse of each number Solve each equation. Check your solution x c a y 3 9. m b Glencoe/McGraw-Hill 323 Mathematics: Applications and Concepts, Course 2

6 MATH-7 Equations [Exam ID:1JZ12K] Scan Number: What is the solution to the number sentence? A 76 B -76 C -48 D 48 x + 14 = What is the value of x that makes the equation true? F 12 G -2 H -12 J 2 x + 5 = 7 3 Solve: A x = 69.4 B x = 7 C x = 6.6 D x = -6.6 x = 38 4 Fran needs to find the solution to the equation 3x + 5 = 17. First Fran will F divide 3x by 3 and divide 17 by 3 G subtract 5 from 5 and subtract 5 from 17 H add 5 to 5 and add 5 to 17 J add 5 to 3 and add 5 to 17

7 5 What is the value of r that makes the following true? A 36 B -36 C 4 D -4 r -3 = 12 6 Which is the solution to the equation represented in the model? F 7 G 5 H 2 J 4 7 There are 24 students in Mrs. Black's class. If the students need to be put into 4 equal groups, how many students will be in each group? A 20 B 6 C 96 D 4 8 Todd makes $550 a week at his job. The company gave Todd a raise and he will receive $634 a week. How much was Todd's raise? F $1,184 G $588 H $84 J $16 9 Thirty two students try out for the basketball team. There are 5 players on the court during a game and the coach wants three times as many players on the team. How many students will NOT be a part of the basketball team? A 49 B 47 C 15 D 17

8 10 What value of g makes the following true? F -33 G 57 H -57 J = g Which is the solution to the equation represented in the model? A 10 B 3 C 2 D 5 12 The Bailey family planned a trip to the drive-in movie theater and 42 family members attended. Seven cars were filled and 7 more people traveled in a truck. How many people were in each car? F 7 G 3 H 5 J 6 13 What value of x makes the equation true? A 28 B C 1 D x = 17

9 14 Jack works at a job earning $11.75 per hour and always tries to put half of his paycheck into his savings account. How many hours will Jack have to work in order to put $ into his savings account? F 20 G 80 H 10 J What value of d makes the following true? A 6 B 4 C 1 4 D.4 48 = 12d 16 Brian and Sue bought a bag of candy to share. If each of them received 18 pieces of candy, how many pieces were originally in the bag? F 18 G 36 H 9 J Sam and five of his friends ordered pizzas and split the bill evenly between them all. If each person paid $5.10, how much was the total bill for the pizzas? A $35.70 B $25.50 C $30.60 D $ Tony works at a department store for 40 hours and makes $ How much does Tony get paid every hour he works? F $46.00 G $8.70 H $40.00 J $11.50

10 19 Tonya works at an ice cream shop for 36 hours and makes $ If p represents her hourly pay, which equation will calculate how much Tonya made per hour? A p = 36 B 36 + p = 297 C 36p = D = 297 p 20 Which value of n makes the following true? 1 F 2 G 20 H 0.2 J 2 40n = What value of x makes the following statement true? A 53 B 43 C 19 D 9 x = 8 22 Due to plate tectonics, the approximate velocity of the Eurasian Plate is 0.95 cm/yr. Henry knows that there are 100 centimeters in one meter and that in a certain amount of years the plate will have moved 19 meters. How many years will be needed for this distance to occur? F 5 G 20 H 95 J 2,000

11 23 Which could be used to find the number y? Six more than a number, y, is equal to eight. A = y B 6 - y = 8 C 6y = 8 D y + 6 = 8 24 What is the solution to the number sentence? F -364 G -162 H 364 J 162 t = The doctor told Katie that she needed to take 2.5 teaspoons of medicine once a day. The medicine filled a bottle with the capacity of 23 teaspoons. If Katie takes the medicine for 9 days, how much medicine will be left in the bottle? A 0.5 teaspoon B 23.0 teaspoons C 22.5 teaspoons D 5.6 teaspoons 26 Carol bought 5 pens of the same type for school and spent $ Which pen did Carol buy? F Pen E G Pen B H Pen A J Pen C

12 27 Eight students are hired to pick up trash in a specific area of town. Each student is given an 80 ft by 100 ft area to clean. What is the total area that is covered by the students? A 64,000 sq ft B 80,000 sq ft C 1,000 sq ft D 1,440 sq ft 28 Quin bought 21 pens of the same type for his classroom and spent $ Which pen did Quin buy? F Pen A G Pen E H Pen C J Pen D 29 John called a plumber to fix a leak in his bathroom. The plumber charged $30 to come to the house and $25 an hour while fixing the leak. If the final bill was $105, how many hours was the plumber at John's house? A 3 B 7 C 4 D 5 30 Rock B has a mass of grams. Rock A is 40 grams more than 5 times the mass of Rock B. What is the mass of Rock A? F 61.5 g G g H g J g

13 31 Denise is mailing a package to a friend. The post office weighed her package and charged $4.90 for the first 6 ounces and $0.13 for each additional ounce. If Denise's package costs $5.81, how much did the package weigh? A 45 ounces B 7 ounces C 13 ounces D 1 ounce 32 What is the solution to the number sentence? F -461 G -203 H 461 J s = Carol has $30 to spend on gasoline for her car. After buying 8 gallons, she has $4 left. How much did each gallon of gasoline cost? A $2.50 B $4.25 C $3.25 D $ Which is the solution to the equation represented in the model? F 6 G 4 H 8 J 2

14 35 Jim will need a total of 48 square feet of carpet to cover his entire basement 1 floor. He currently has of the total amount of carpet that he needs. How much 4 more carpet does Jim need to purchase in order to finish his basement floor? A 12 sq ft B 36 sq ft C 24 sq ft D 30 sq ft 36 Look at the equation shown in the model. Which model shows the next step in solving the equation? F H G J 37 Which is the solution to the equation represented in the model? A -6 B -8 C -10 D -2

15 38 Which could be used to find the number x? One less than twice a number, x, is equal to four. F 2x - 4 = 1 G 2x - 1 = 4 H 1-2x = 4 J x - 1 = 4 39 What is the solution to 32 = -4-12x? A 40 B -2.3 C -2 D Nicholas is 7 years older than Travis. If Nicholas is 10 years old, what is Travis' age? F 17 G 3 H 4 J 20

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