Name Unit Linear Equations Test Date Pd LINEAR

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Name ___________________ Unit: Linear Equations Test Date ______________ Pd ______ LINEAR EQUATIONS UNIT TEST

Name ___________________ Unit: Linear Equations Test Date ______________ Pd ______ LINEAR EQUATIONS UNIT TEST INSTRUCTIONS: Solve the problems below. Be sure to show your thinking. 1. 75 x – 2 3. Austin solved the equation as shown below. Which describes the error that Austin made in his work? Austin's Work: -3 + 7 x – 9 + 8 x = 54 15 x – 6 = 54 15 x = 60 x = 4 A. Austin did not combine 7 x and 8 x correctly. B. Austin did not combine -3 and -9 correctly. C. Austin did not divide correctly. D. Austin did not make an error in his work. 5. A video game store allows customers to rent games for $4. 75 each. Customers can also buy a membership for $54 annually, and video games would only cost $2. 50 each. Write and solve an equation to find the number of video games a customer would have to rent in a year in order for the two options to be equal. Equation: ______________ Solution: ______________ ©Maneuvering the Middle LLC, 2017

Solve the problems below. Be sure to show your thinking. 6. Solve the equation

Solve the problems below. Be sure to show your thinking. 6. Solve the equation below. 7. Solve the equation below. 14 x – 34 = 11 x + 29 -4 – 0. 2 x + 11 = -0. 8 x + 10 x = _______________ x x x -1 -1 = -1 -x -x -1 -1 -1 9. Joe’s Catering Company charges a $45 set-up fee plus $12. 50 person. Jimmy’s catering company charges a $75 set up fee plus $7. 50 person. Which inequality could be used to determine x, the number of people for which Joe’s Catering Company would be less expensive than Jimmy’s catering company? A. 45 + 12. 5 x > 75 + 7. 5 x B. 45 + 12. 5 x ≥ 75 + 7. 5 x C. 45 + 12. 5 x < 75 + 7. 5 x D. 45 + 12. 5 x ≤ 75 + 7. 5 x 11. The rectangles shown below have the same perimeter. Which of the following is the value of x? A. x = 15 B. x = 12 C. x = -2. 64 3 x – 7. 5 5 x + 5. 25 1. 4 x 4. 25 x D. x = 3. 25 ©Maneuvering the Middle LLC, 2017

Solve the problems below. Be sure to show your thinking. 12. Which of the

Solve the problems below. Be sure to show your thinking. 12. Which of the following is the value of x needed to make the equation true? -18 + 3 x + x = -4 x + 50 A. x = 11. 3 B. x = 4. 5 C. x = 8. 5 D. x = -4. 5 14. Mike is driving a boat at 12 mph and is increasing his speed by 0. 2 mph each second. Hank is driving a boat at 25 mph and is decreasing his speed by 0. 7 mph each second. Which of the following equations could be used to determine x, the number of seconds it will take for the boats to be traveling the same speed? A. 12 x + 0. 2 = 25 x – 0. 7 C. 12. 2 x = -25. 7 x B. 12 – 0. 2 x = 25 + 0. 7 x D. 12 + 0. 2 x = 25 – 0. 7 x 15. Norah has never lost a tooth, but she will receive $0. 75 from the tooth fairy each time she loses a tooth. Kate has $1. 25 from the tooth fairy, and she gets $0. 25 each time she loses a tooth. Which inequality could be used to find x, the number of teeth that each girl would have to lose for Norah to have at least as much money from the tooth fairy as Kate? 16. Which of the following equations does not have a solution of x = 0. 5? A. 0. 75 x ≥ 1. 25 + 0. 25 x B. -2 x + 6 = -6 x + 8 B. 0. 75 x ≥ 1. 25 – 0. 25 x C. 0. 75 x ≤ 1. 25 + 0. 25 x D. 0. 75 x > 1. 25 + 0. 25 x A. 10 x – 5 = -2 x + 1 C. -5 x + 10 = x + 7 D. 3 x + 3 = -2 x + 13 ©Maneuvering the Middle LLC, 2017

Solve the problems below. Be sure to show your thinking. 18. Find the value

Solve the problems below. Be sure to show your thinking. 18. Find the value of x needed to make the equation true. -7. 2 x + 3. 5 = -8. 7 x – 10 19. A tree in Micah’s yard has 120 leaves and loses an average of 4. 5 leaves each day. A tree in Heather’s yard has 45 leaves and gains an average of 0. 5 leaves each day. Write and solve an equation to find the number of days it will take for both trees to have an equal number of leaves. Equation: _______________ x = ________ Solution: _______________ ©Maneuvering the Middle LLC, 2017