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Mastering Linear Equations and Inequalities Practice

Enhance your understanding of linear equations, inequalities, and compound inequalities with targeted practice. This set of problems includes absolute value equations and various scenarios, such as solving equations for variables like m, w, and c, as well as evaluating compound inequalities. Each question presents multiple-choice answers, allowing you to test your skills and deepen your comprehension. Perfect for students aiming to improve their math proficiency in equations and inequalities!

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Mastering Linear Equations and Inequalities Practice

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  1. EOC Practice #14 SPI 3102.3.5

  2. EOC Practice #14 • Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value.

  3. Solve the equation = 7 • for m. A. m = 50 B. m = 8 C. m = 10 D. m = 0

  4. Solve the equation w – 4 = –12 – 3w • for w. A. w = –4 B. w = –2 C. w = –8 D. w = 4

  5. Solve the equation c – (–1.3) = –2.3 • for c. A. c = –1.0 B. c = 3.6 C. c = 1.0 D. c = –3.6

  6. Which number is a solution to • 12x – 7 > 7x + 13 or 4x + 5 > 7x + 35? A. –12 B. –10 C. –4 D. 4

  7. Which compound inequality • represents │7 + 2n │≥19 ? A. 7 + 2n ≥ 19 or 7 + 2n ≥ –19 B. 7 + 2n ≥ 19 or 7 + 2n ≤ –19 C. –19 ≤ 7 + 2n ≤ 19 D. 7 + 2n ≤ 19 or 7 + 2n ≥ –19

  8. Solve 4b – 3(2b – 6) > 3 – (5b + 9) • for b. A. b < 8 B. b > 8 C. b < –8 D. b > –8

  9. Solve 8 > 5 – 3x and 5 – 3x > –13 for x. A. B. C. D.

  10. 8. Solve │x – 6 │ = 4. • {2, 10} • {–2, 10} • {–2, –10} • {–2, 2}

  11. 9. Solve: 7x – 11 < 10 < 3x + 28. A. x < 3 or x < 6 B. –6 < x < 3 C. x > 6 and x < 3 D. –3 < x < 6

  12. 10. Which statement represents the solution to this compound inequality? –2x – 7 ≥ 3 or –4x + 6 ≤ –18 A. x ≤ 5 or x ≤ –6 B. x ≥ –5 or x ≤ 6 C. x ≤ –5 or x ≥ 6 D. x ≤ 5 or x ≥ –6

  13. The Answers

  14. Solve the equation = 7 • for m. A. m = 50 B. m = 8 C. m = 10 D. m = 0

  15. Solve the equation w – 4 = –12 – 3w • for w. A. w = –4 B. w = –2 C. w = –8 D. w = 4

  16. Solve the equation c – (–1.3) = –2.3 • for c. A. c = –1.0 B. c = 3.6 C. c = 1.0 D. c = –3.6

  17. Which number is a solution to • 12x – 7 > 7x + 13 or 4x + 5 > 7x + 35? A. –12 B. –10 C. –4 D. 4

  18. Which compound inequality • represents │7 + 2n │≥19 ? A. 7 + 2n ≥ 19 or 7 + 2n ≥ –19 B. 7 + 2n ≥ 19 or 7 + 2n ≤ –19 C. –19 ≤ 7 + 2n ≤ 19 D. 7 + 2n ≤ 19 or 7 + 2n ≥ –19

  19. Solve 4b – 3(2b – 6) > 3 – (5b + 9) • for b. A. b < 8 B. b > 8 C. b < –8 D. b > –8

  20. Solve 8 > 5 – 3x and 5 – 3x > –13 for x. A. B. C. D.

  21. 8. Solve │x – 6 │ = 4. • {2, 10} • {–2, 10} • {–2, –10} • {–2, 2}

  22. 9. Solve: 7x – 11 < 10 < 3x + 28. A. x < 3 or x < 6 B. –6 < x < 3 C. x > 6 and x < 3 D. –3 < x < 6

  23. 10. Which statement represents the solution to this compound inequality? –2x – 7 ≥ 3 or –4x + 6 ≤ –18 A. x ≤ 5 or x ≤ –6 B. x ≥ –5 or x ≤ 6 C. x ≤ –5 or x ≥ 6 D. x ≤ 5 or x ≥ –6

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