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Solving Inequalities using Addition and Subtraction

Learn how to solve inequalities using addition and subtraction operations. Practice problems and step-by-step solutions provided.

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Solving Inequalities using Addition and Subtraction

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  1. ObjectiveThe student will be able to: • solve inequalities using addition and subtraction. SOL: A.3 Designed by Skip Tyler, Varina High School

  2. o 29 30 31 7) Solve x + (-14) < 16 Solve this problem like an equation • Draw “the river” • Eliminate double signs • Add 14 to both sides • Simplify • Check your answer • Graph the solution x- 14< 16 + 14 + 14 x < 30 30 + (-14) = 16 16 = 16

  3. ● -15 -14 -13 8) Solve y + 21 ≥ 7 • Draw the “river” • Subtract 21 from both sides • Simplify • Check your answer • Graph the solution - 21 -21 y ≥ -14 30 + (-14) = 16 16 = 16

  4. o 16 17 18 9) Solve 8y + 3 > 9y - 14 - 8y - 8y 3 > y - 14 + 14 + 14 17 > y y < 17 8(17) + 3 = 9(17) - 14 • Draw “the river” • Subtract 8y from both sides • Simplify • Add 14 to both sides • Simplify • Rewrite inequality with the variable first • Check your answer • Graph the solution

  5. ● 30 31 32 10) Solve 3r - 17 ≥ 2r + 14 - 2r - 2r r – 17 ≥ 14 + 17 + 17 r ≥ 31 3(31) - 17 = 2(31) + 14 • Draw “the river” • Subtract 2r from both sides • Simplify • Add 17 to both sides • Simplify • Check your answer • Graph the solution

  6. Answer Now 11) Solve -2x + 6 ≥ 3x - 4 • x ≥ -2 • x ≤ -2 • x ≥ 2 • x ≤ 2

  7. Answer Now 12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? • 96 • 97 • 98 • 100

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