1. Solving linear equations[1].docx

Solving linear equations 1. Solve for k: k + 22 = 29 k = Correct answer: 7 Difficulty level: 1 2. Solve for n: -8 + n = 23 n = Correct answer: 31 Difficulty level: 1 3. Solve for x: x – 9 = 1 x = Correct answer: 10 Difficulty level: 1 4. Solve for n: 18 = n - 18 n = Correct answer: 36 Difficulty level: 1 5. Solve for k: k + 10 = 27 k = Correct answer: 17 Difficulty level: 1 6. Solve for t: t + 25 = 26 t = Correct answer: 1 Difficulty level: 1 7. Solve for k: -30 + k = 22 k = Correct answer: 52 Difficulty level: 1 8. Solve for k: 19 = 14 + k k = Correct answer: 5 Difficulty level: 1 9. Solve for q: 3 = -8 + q q = Correct answer: 11 Difficulty level: 1 10. Solve for p: 10 = -19 + p p = Correct answer: 29 Difficulty level: 1 11. Solve for r: -12 + r = 7 r = Correct answer: 19 Difficulty level: 1 12. Solve for p: p + 12 = 30 p = Correct answer: 18 Difficulty level: 1 13. Solve for p: p – 18 = 3 p = Correct answer: 21 Difficulty level: 1 14. Solve for k: 30 = k + 23 k = Correct answer: 7 Difficulty level: 1 15. Solve for y: 25 = -14 + y y = Correct answer: 39 Difficulty level: 1 16. Solve for r: 20 = r + 11 r = Correct answer: 9 Difficulty level: 1 17. Solve for z: -26 + z = 15 z = Correct answer: 41 Difficulty level: 1 18. Solve for p: 29 = p + 20 p = Correct answer: 9 Difficulty level: 1 19. Solve for y: 24 = y + 19 y = Correct answer: 5 Difficulty level: 1 20. Solve for n: 27 = 15 + n n = Correct answer: 12 Difficulty level: 1 21. Solve for k: 2 = -30 + k k = Correct answer: 32 Difficulty level: 1 22. Solve for n: 19 + n = 30 n = Correct answer: 11 Difficulty level: 1 23. Solve for k: 18 + k = 30 k = Correct answer: 12 Difficulty level: 1 24. Solve for r: 25 = 7 + r r = Correct answer: 18 Difficulty level: 1 25. Solve for p: 2 = -1 + p p = Correct answer: 3 Difficulty level: 1 26. Solve for r: 17 = r +10 r = Correct answer: 7 Difficulty level: 1 27. 12s≤4(s-2) Which of the following best describes the solutions to the inequality shown above? A. s≤-1 B. s≤-23 C. s≥-14 D. s≥8 Correct answer: A Difficulty level: 2 28. 4c+5<4c+3 Which of the following best describes the solutions to the inequality shown above? A. All real numbers B. c<12 C. c>14 D. No solution Correct answer: D Difficulty level: 2 29. If 9≥4x+1, which inequality represents the possible range of values of 12x+3? A. 12x+3≥17 B. 12x+3≤17 C. 12x+3≥27 D. 12x+3≤27 Correct answer: D Difficulty level: 2 30. 6=-s+77 Given the above equation, what is the value of 1+5(77-s)? A. -739 B. -29 C. 31 D. 741 Correct answer: C Difficulty level: 2 31. If 16-7w=w+14-6w, what is the value of w-1? A. w-1=-2 B. w-1=0 C. w-1=1 D. w-1=-3 Correct answer: B Difficulty level: 2 32. If 12+25s=s-34 , what is the value of s? A. s=34 B. s=2512 C. s=-2512 D. s=-34 Correct answer: B Difficulty level: 2 33. 10(23+7)=100l+100l What is the value of ℓ in the equation above? Correct answer: 3/2 Difficulty level: 2 34. -p+60=-h+10000 In the equation above, h is a constant. If p=10 is a solution to the equation, what is the value of h? Correct answer: 9950 Difficulty level: 2 35. 15x-3=9x+1 Which of the following is the solution to the equation shown above? A. x=16 B. x=-23 C. x=23 D. x=1 Correct answer: C Difficulty level: 2 36. 4+5m=4m+1+m Which of the following best describes the solution set to the equation shown above? A. The equation has exactly one solution, m=0. B. The equation has exactly one solution, m=1. C. The equation has no solutions. D. The equation has infinitely many solutions. Correct answer: C Difficulty level: 2 37. If 15bx-20>35, where b is a positive constant, what is the possible range of values of 4−3bx? A. Any value less than −7 B. Any value greater than −7 C. Any value less than-113bx D. Any value greater than 113bx Correct answer: A Difficulty level: 2 38. If -k+78=98-20, then what is the value of k? Correct answer: 0 Difficulty level: 3 39. 2(4p+1)5≤3+12p4 Which of the following best describes the solutions to the inequality shown above? A. p ≤-137 B. p ≥-137 C. p ≤-14 D. p ≥-14 Correct answer: D Difficulty level: 3 40. -4+bx=2x+3(x+1) In the equation shown above, b is a constant. For what value of b does the equation have no solutions? A. 3 B. 4 C. 5 D. 6 Correct answer: 5 Difficulty level: 3 41. 32q≤92q-18 Which of the following best describes the solutions to the inequality shown above? A. q ≤ 3 B. q ≥ 3 C. q ≤ 6 D. q ≥ 6 Correct answer: D Difficulty level: 3 42. If 9<15mx-8<27, where m is a positive constant, what is the possible range of values of 83-5mx? A. Any value greater than −3 or less than −9 B. Any value greater than −9 and less than −3 C. Any value greater than -73m or less than​​ -1715m D. Any value greater than -1715m and less than -73m Correct answer: B Difficulty level: 3 43. -3(x+3)-8=6-4x Which of the following is the solution to the equation shown above? A. x = 17 B. x = -23 C. x = 23 D. x = 11 Correct answer: C Difficulty level: 3 44. If 3(r+300)=6, then what is the value of r+300-2? Correct answer: 0 Difficulty level: 3 45. 3t+1=-12-5t Which of the following best describes the solution set to the equation shown above? A. The equation has no solutions. B. The equation has exactly one solution, t = -716 C. The equation has exactly one solution, t = -74 D. ​The equation has infinitely many solutions. Correct answer: B Difficulty level: 3 46. If 5<2x+3<11, what is the possible range of values of -4x-6? A. Any value greater than−10 or less than −22 B. Any value greater than −22 and less than −10 C. Any value greater than 1 and less than 4 D. Any value greater than 4 or less than 1 Correct answer: B Difficulty level: 3 47. 4-13z=-7z+6 Which of the following is the solution to the equation shown above? A. z=310 B. z=-310 C. z=203 D. z=206 Correct answer: A Difficulty level: 3 48. If 153=2(z+z)n, then what is the value of 2n(2z)-193? A. -113 B. -40 C. 40 D. 113 Correct answer: B Difficulty level: 3 49. 4|6+2s|-27≤-3 Which of the following best describes the solutions to the inequality shown above? A. -24≤s≤0 B. -6≤s≤0 C. s≤0 or s≥3 D. No solution Correct answer: B Difficulty level: 4 50. 4x+1=-ax-4 In the equation shown above, a is a constant. Which of the following values of a results in an equation with exactly one solution? A. 4 B. -4 C. Neither value D. Both values Correct answer: A Difficulty level: 4 51. 4(80+n)=(3k)n In the equation above, k is a constant. For what value of k are there no solutions to the equation? Correct answer: 4/3 Difficulty level: 4 52. 8-9x+1=ax+4 In the equation shown above, a is a constant. Which of the following values of a results in an equation with exactly one solution? A. 9 B. 8 C. Neither value D. Both values Correct answer: D Difficulty level: 4 53. 4(x-2)+x=ax-8 In the equation shown above, a is a constant. Which of the following values of a results in an equation with exactly one solution? A. 4 B. 5 C. Neither value D. Both values Correct answer: A Difficulty level: 4 54. -2(x+2)=6-ax In the equation shown above, a is a constant. Which of the following values of a results in an equation with exactly one solution? A. -2 B. 2 C. Neither value D. Both values Correct answer: A Difficulty level: 4 55. 2x-1=-1+ax In the equation shown above, a is a constant. Which of the following values of a results in an equation with exactly one solution? A. 2 B. 3 C. Neither value D. Both values Correct answer: B Difficulty level: 4 56. 4-3y=6y+4-9y Which of the following best describes the solution set to the equation shown above? A. The equation has no solutions. B. The equation has exactly one solution, y=0. C. The equation has exactly one solution, y=43. D. The equation has infinitely many solutions. Correct answer: D Difficulty level: 4 57. 17+27=-7w Given the above equation, what is the value of 10(-21w+1)? Correct answer: 1330 Difficulty level: 4