Math Equations Test Review Key

Algebra 1 Equations Test Review Name: Key Assignment 3.1-3.6 Check whether the given number is a solution to the equation. Write “Yes” or “No” 1. 22 = 14 + 8 Yes 2. 4 + 9 = 5 No Solve the following equations. 3. y - 15 = -4 y = 11 4. 7 + x = -3 x = -10 5. t - (-10) = 2 t + 10 = 2 t = -8 6. x + 9 + 15 = 30 + 12 x + 24 = 42 x = 18 7. t + 1/4 = 3/4 t = 1/2 8. 10 = -x - 8 - 6 10 = -x - 14 24 = -x x = -24 Find the length of the side marked x. 9. The perimeter is 37 feet. 37 = 10 + 17 + 4 + x 7 = 31 + x -31 -31 x = -24 ft. 10. 81/3 = 3t/2 t = 27 11. -6x/6 = 54/-6 x = -9 12. x/4 = -16 - 1 x = -64 13. m/8 = -5 m = -40 14. 32/4 = 8 9 = 24 15. 6/3 = -3 x = -5 16. You purchased 8 copies of a poster that reads “Math Rocks My Socks” and paid $78. How much did each poster cost? 8x = 78 x = $9.75 Solve the following multi-step equations. 17. 26 + 9x = -1 -26 -26 9x = -27 x = -3 18. -32 = 4c - 12 +12 +12 -20 = 4c c = -5 19. 9r - 2 - 6r = 1 3r - 2 = 1 +2 +2 3r = 3 r = 1 20. -2(x - 7) - 5 = 7 -2x + 14 - 5 = 7 -2x + 9 = 7 -2x = -2 x = 1 21. 17 = n + 3(1 + 2n) 17 = n + 3 + 6n 17 = 7n + 3 14 = 7n n = 2 22. 3(x + 8) = 9 3x + 24 = 9 3x = -15 x = -5 23. 2x/3 - 9 = -6 2x/3 = 3 2x = 9 x = 9/2 24. 4y - (2y + 7) = 7 4y - 2y - 7 = 7 2y - 7 = 7 2y = 14 y = 7 25. -30 = -3(4 + x) + 5 -30 = -12 - 3x + 5 -30 = -7 - 3x -23 = -3x x = 23/3 26. It takes 64 inches of ribbon to make a bow and wrap the ribbon around a box. The bow takes 30 inches of ribbon. The width of the box is 12 inches. What is the height of the box? 30 + 2(12) + 2h = 64 30 + 24 + 2h = 64 54 + 2h = 64 2h = 10 h = 5 inches Solve the equation if possible. Determine whether the equations has one solution, no solution, or is an identity. 27. 3x - 9 = 3x -9 = 0 No Solution 28. 23y - 15y = -15y 8y = -15y 0 = -23y No Solution 29. 2m - 9 = 6 - m 3m - 9 = 6 3m = 15 m = 5 One 30. 36 - 4d = 4(9 - d) 36 - 4d = 36 - 4d Identity 31. 12 + 11h = -18 - 4h 12 + 15h = -18 15h = -30 h = -2 One 32. 2x + 18 + 4x = -2x + 10 6x + 18 = -2x + 10 8x + 18 = 10 8x = -8 x = -1 One 33. On one side of a scale there are 6 calculators, 3 weighting 1 pound each and 3 weighting x pounds each. The scale is balanced if 5 calculators weighting x pounds each are placed on the other side of the scale. How much does each of the unknown calculators   weigh? 3 + 3x = 5x 3 = 2x x = 1.5 pounds Solve the following equations. 34. 4x + 2(x - 9) = 54 4x + 2x - 18 = 54 6x - 18 = 54 6x = 72 x = 12 35. 3a + 2(a - 1) = 7a - 4(a + 2) 5a - 2 = 3a - 8 2a - 2 = -8 2a = -6 a = -3 36. -10x - 42 = 12 - 3x -7x - 42 = 12 -7x = 54 x = -6 37. (8x + 15)/3 = (4x + 12)/5 5(8x + 15) = 3(4x + 12) 40x + 75 = 12x + 36 28x + 75 = 36 28x = -39 x = -39/28 38. 3/5(15y - 20) = 2(2y + 8) 9y - 12 = 4y + 16 5y - 12 = 16 5y = 28 y = 28/5 39. 9(20 - 12t) = 8(6 + 9t) - 24t 180 - 108t = 48 + 72t - 24t 180 - 108t = 48 + 48t 132 = 156t t = 11/13 40. You are making sandwiches to sell at a fundraiser. It costs $0.90 to make each sandwich plus a one-time cost of $24 for packaging. You plan to sell each sandwich for $2.50. Write and solve an equation to find how many sandwiches you need to sell to break even.   0.90x + 24 = 2.50x 24 = 1.6x x = 15 sandwiches to sell Solve the following equations. Round your answer to the nearest hundredth. 41. 3x - 4 = 7 3x = 11 x = 2.33 42. 5x - 9 = 18x - 23 4 = 13x x = 1.08 43. 13.7t - 4.7 = 9.9 + 8.1t 5.6t = 14.6 t = 2.61 Solve the following equations. Round your answer to the nearest tenth. 2.7 - 3.6x = 8.4 + 23.7x -5.7 = 27.3x x ≈ -0.2 2(x - 6) = 5x + 7 2x - 12 = 5x + 7 -13 = 3x x ≈ -4.3 14(3 - 7y) = -(9 + 2y) 42 - 98y = -9 - 2y 51 = 96y y ≈ 0.5 A rope 10.3 centimeters long is cut into 4 pieces of equal length. What is the length of each piece? 10.3 / 4 = 2.575 Each piece is 2.575 cm You are saving money for the purchase of a new bike. You have saved $78.23. The bike costs $152.95. How much more money do you need? 1 x = Money still needed 78.23 + x = 152.95 x = 74.72