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Problem-solving Inequalities Quick Guide

Learn how to solve multi-step inequalities with clear rules, examples, and visual aids on a number line. Master the process with step-by-step instructions and practice problems to improve your algebra skills.

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Problem-solving Inequalities Quick Guide

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  1. Algebra Bell-work 9/13/17 Turn in your HW! 1.) 7x – 6 = 2x + 9 2.) -2x > 10 (Check your answer!)

  2. 1-6: Solving Multi-step Inequalities Rules for solving inequalities: 1.) Solve same way as a regular equation, but your answer is more of a solution set. (You can have more than one answer that makes the inequality true.) 2.) Graph the solution on a number line:

  3. 1-6: Solving Multi-step Inequalities 2.) Graphing the solution on a number line:

  4. o 3 4 5 1) Solve 5m - 8 > 12 + 8 + 8 5m > 20 5 5 m > 4 5(4) – 8 = 12

  5. o -3 -2 -1 2) Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 a < -2 12 - 3(-2) = 18

  6. Which graph shows the solution to 2x - 10 ≥ 4? • .

  7. ● -8 -7 -6 4) Solve 2r - 18 ≤ 5r + 3 -2r -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3 -7 ≤ r or r ≥ -7 2(-7) – 18 = 5(-7) + 3

  8. 5) Solve

  9. Special Case #1 • Distribute • Combine like terms • Get variable on same side • True or false? 3x + 4 > 2(x + 3) + x 3x + 4 > 2x + 6 + x 3x + 4 > 3x + 6 -3x -3x 4 > 6 This statement is FALSE: No Solution

  10. Special Case #2 • Distribute • Combine like terms • Get variable on same side • True or false? 3 – 3(y – 2) < 13 – 3(y – 6) 3 – 3y + 6 < 13 – 3y + 18 -3y + 9 < -3y + 31 +3y + 3y 9 < 31 This statement is TRUE: All Real Solutions

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