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Solving Inequalities
Lesson 1
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Lesson 1: 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\ge\frac{c-b}{a}

Worked example

−4x−8≤−8⇒x≥0-4x-8\le-8\Rightarrow x\ge0

Checkpoint

Find the boundary for 7x+1<78\text{Find the boundary for }7x+1<78

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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