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Solving Inequalities
Lesson 3
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Lesson 3: 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\gec⇒x≥c−baax+b\gec\Rightarrow x\ge\frac{c-b}{a}

Worked example

8x+8≥104⇒x≥128x+8\ge104\Rightarrow x\ge12

Checkpoint

Find the boundary for 6x−3≥−9\text{Find the boundary for }6x-3\ge-9

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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