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Name: _______________________________________ Block: _____ Review for Solving Equations and Inequalities Retest Solve each equation. Show your work! Leave all answers as integers or fractions. 1. x + (-9) = 13 2. 5 – 2x = 3x + 8 x = 22 x=- 3. ⅔(18x – 21) = 7 – 3(x – 3) 4. 5(2 – x) + 7x = -3(x + 5) x= 5. x = -5 ( ) 6. x = -36 no solution x = - 45 7. 8. y = -11 x = -35 9. 10. ⅔(9x – 6) = 10x – 4(x + 1) + 5 = -2 x = 28 All Real numbers Solve each inequality. Show your work! Leave all answers as integers or fractions. 11. -4 12. x<8 13. -7 x > - 35 x < -39 14. - 3x > 27 x < -65 15. 2(x + 6) < 2x + 2 x<-9 16. -3(x +2) < -3x +10 12 < 2 No Solution 17. 8y – 5 > -6y + 1 - 6 < 10 All Real Numbers 18. 8 - 8x < 40 y> x>-4 19. 8(x – 1) > -8 + 8x 20. -3(2x – 1) -8 >-8 No Solution x > -1 1 – 8x Solve The Following Compound Inequalities. Graph their Solutions. 21. -6<k<1 -6 1 22. v > 2 or v < 1 1 2 23. 40 < 5p – 10 or 3p + 6 < 42 p > 10 or p < 12 All real numbers 10 12 24. Fill in the property that justifies each step. 14 = 2(x – 3) 14 = 2x – 6 Distributive Property 14 + 6 = 2x – 6 + 6 Add. Property of Equality 20 = 2x + 0 Additive Inverse 20 = 2x Additive Identity Given Multiplication Property of Equality 10 = 1x Multiplicative Inverse 10 = x Multiplicative Identity x = 10 Symmetric Property 25. Fill in the property that justifies each step. Solution (3x + 9) + 1 > 13 Property Given 3x + (9 + 1) > 13 Associative Property of Addition 3x + 10 > 13 Substitution 3x + 10 + (-10) > 13 + (-10) Addition Property of Inequality 3x + 0 > 3 Additive Inverse 3x > 3 Additive Identity 3x > Multiplication Property of Inequality 3 1x > 1 Multiplicative Inverse x>1 Multiplicative Identity 26. There are four mistakes in the proof below. Find and correct the mistakes. (x + 3) 5 > -10 Given 5(x + 3) > -10 Associative Property of Multiplication Commutative 5x + 15 > -10 Distributive Property 5x + 15 + (-15) > -10 + (-15) Addition Property of Equality Inequality 5x + 0 > -25 Inverse Property of Multiplication Addition 5x > -25 Identity Property of Addition 5x > -25 • Multiplication Property of Inequality 1x > -5 Identity Property of Multiplication Inverse x>-5 Identity Property of Multiplication