Double Inequalities (Leaving Cert Mathematics): Flashcards

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Double Inequalities
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What are double inequalities?

Inequalities with two inequality signs

Method to solve double inequalities

Solve both inequalities separately

Left inequality from 3x≤5x+3≤233x\le 5x+3 \le 23

3x≤5x+33x\le 5x+3

Solution to 3x≤5x+33x\le 5x+3

x≥−32x \ge -\frac{3}{2}

Effect of dividing by negative on inequality sign

Flip the sign

Right inequality from 3x≤5x+3≤233x\le 5x+3 \le 23

5x+3≤235x+3 \le 23

Solution to 5x+3≤235x+3 \le 23

x≤4x \le 4

Combined solution for 3x≤5x+3≤233x\le 5x+3 \le 23

−32≤x≤4-\frac{3}{2} \le x \le 4

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