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Solving Inequalities
Lesson 2
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Lesson 2: 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\lec⇒x≤c−baax+b\lec\Rightarrow x\le\frac{c-b}{a}

Worked example

7x−8≤−71⇒x≤−97x-8\le-71\Rightarrow x\le-9

Checkpoint

Find the boundary for −6x+12≤36\text{Find the boundary for }-6x+12\le36

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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