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Pre-Algebra, Unit 03 Practice Test: Multi-Step Equations and Inequalities Name: Date: 1. Define inequality and give an example. 2. Define solution of an inequality. 3. Are −2 x < 8 and x < −4 equivalent inequalities? Why or why not? 4. When graphing an inequality, when do you decide to ‘shade in’ the circle at the coordinate on the number line? 5. (SE) Which of the following would be the best choice for the first step in solving for x in the equation below? 2 x + 8 =−10 A. B. C. D. add 8 to both sides of the equation subtract 8 from both sides of the equation multiply both sides of the equation by 2 divide both sides of the equation by −2 6. (SE) What is the value of x that satisfies the equation −3x − 6 = 30 ? A. B. C. D. −12 −8 8 12 HS Pre-Algebra Practice Test Unit 03: Multi-Step Equations and Inequalities Revised 2013 - CCSS Page 1 of 6 7. (SE) Five less than twice a number is fifty-three. What is the number? A. B. C. D. −29 −24 24 29 8. (SE) What is the solution to the equation below? −3(2 x − 7) + 4 x = 15 3 −4 −11 −18 A. B. C. D. 9. (SE) What value of x makes the equation below true? 5 x + 4 = 9 x − 12 A. B. C. D. −4 −2 2 4 10. (SBAC) Three students solved the equation 3(2 x + 3) = 21 in different ways, but each student arrived at the correct answer. Select all of the solutions that show a correct method for solving the equation. A. 3(2 x + 3) =21 6 x + 9 =21 6x 9 21 + = 6 6 6 9 9 − = − 6 6 12 x= 6 x= 2 B. 1 1 ⋅ 3(2 x + 3) = 21 ⋅ 3 3 2 x + 3 =7 −3 =−3 2x 4 = 2 2 x=2 C. 3(2 x + 3) = 21 5 x + 9 =21 + 9 =+ 9 15 x = 30 15 x 30 = 15 15 x=2 11. Solve −2 x + 3 = 5 x − 18 . Show your work. HS Pre-Algebra Practice Test Unit 03: Multi-Step Equations and Inequalities Revised 2013 - CCSS Page 2 of 6 12. (SE) A music website sold 68 single songs and 40 albums today. The number of single downloads has been increasing by 12 each day. The number of album downloads has been decreasing by 2 each day. If these trends continue, in how many days will the numbers of single downloads be five times the number of album downloads? A. 28 days B. 18 days C. 6 days D. 2 days 13. Solve and graph 4 x − 2 > 10 . Show your work. −5 0 5 14. Which number line graph represents the solution of the inequality below? −3 < x − 4 A. B. −5 0 5 −5 0 5 −5 0 5 −5 0 5 C. D. 15. Solve the inequality for x. −6 x ≥ −36 A. B. C. D. x ≥ −6 x ≤ −6 x≥6 x≤6 16. What values of x satisfy the inequality A. B. C. D. x + 4 < −8 ? 3 x < −4 x > −4 x < −36 x > −36 HS Pre-Algebra Practice Test Unit 03: Multi-Step Equations and Inequalities Revised 2013 - CCSS Page 3 of 6 17. (SE) The cost of renting a car is $65 per day plus $0.25 per mile. Another rental agency charges $80 per day, but only $0.20 per mile. How many miles would you have to drive to make the total cost of renting the car the same at both companies? A. B. C. D. 100 miles 290 miles 300 miles 325 miles 18. Your club is going to make and sell cookies as a fund raiser. You buy ingredients for $33.25 and a sign for $2.50. You will sell each cookie for $0.50. Which inequality could you use to determine the number of cookies (c) you must sell to earn a profit of at least $50 ? A. B. C. D. 0.5c + 35.75 ≥ 50 0.5c − 35.75 ≥ 50 0.5c + 35.75 ≤ 50 0.5c − 35.75 ≤ 50 19. (SBAC) For each linear equation in this table, indicate whether the equation has no solution, one solution, or infinitely many solutions. Equation No Solution One Solution 4 x − 1 =−4 x + 1 3 x + 11 = 3 x − 11 4(3 x + 2) = 12 x + 8 2x + 5 = 5 Infinitely Many Solutions 20. (SE/SBAC) Choose the best values for P and Q so that the equation will have no solutions. 2 + 6 ( 2 x − 1= ) 4 ( Px + Q ) A. P = 3 and Q = –1 B. P = 3 and Q = 1 C. P = 2 and Q = –1 D. P = 2 and Q = 1 HS Pre-Algebra Practice Test Unit 03: Multi-Step Equations and Inequalities Revised 2013 - CCSS Page 4 of 6 21. (SE) The table shows the annual fee at two golf courses and the fee each time a member plays a round of golf. Course Costs A. Write and solve an equation to determine the Course Annual Fee for 1 number of rounds of golf for which the total cost Fee Round for 1 year at Course M is equal to Course Q. M $600 $20 Show your work. Q $450 $25 B. You are able to play an average of 2 rounds of golf per month. For the year, which course would be the most economical to play? Explain your thinking. Long term memory review: 22. Name the quadrant in which the point ( −2,1) lies. 23. Simplify the expression 3(2a + 1) + a. 24. You are given= a 0.7b − 1.9 ; what is the value of a when the value of b is 14? A. 11.7 B. 9.8 C. 8.9 D. 7.9 HS Pre-Algebra Practice Test Unit 03: Multi-Step Equations and Inequalities Revised 2013 - CCSS Page 5 of 6 BONUS: (HSPE) The graph below represents the solution set of an equation. -8 -6 -4 -2 0 2 4 6 8 Which of these is the equation? A. x =2 B. x =6 C. x+2 = 4 D. x+2 = 6 HS Pre-Algebra Practice Test Unit 03: Multi-Step Equations and Inequalities Revised 2013 - CCSS Page 6 of 6