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Solving Inequalities
Lesson 8
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Lesson 8: Solving Linear Inequalities

Find boundary values and preserve inequality truth.

Inequalities solve like equations with one critical rule: when multiplying or dividing by a negative number, flip the inequality sign.

Key formula

ax+b>c⇒x>c−baax+b>c\Rightarrow x>\frac{c-b}{a}

Worked example

7x−10>4⇒x>27x-10>4\Rightarrow x>2

Checkpoint

Find the boundary for −5x+9>−41\text{Find the boundary for }-5x+9>-41

Recap

  • - Solve the boundary by replacing inequality with equals.
  • - Flip direction only when dividing/multiplying by negatives.
  • - Express answer with correct boundary relation.
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