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Solving Inequalities
Lesson 7
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Lesson 7: 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−6>−83⇒x<11-7x-6>-83\Rightarrow x<11

Checkpoint

Find the boundary for 4x−5<47\text{Find the boundary for }4x-5<47

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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