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Solving Inequalities
Lesson 6
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Lesson 6: 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

−5x>5⇒x<−1-5x>5\Rightarrow x<-1

Checkpoint

Find the boundary for −7x−12≤−96\text{Find the boundary for }-7x-12\le-96

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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