1Cademy - Try It: Solving and Graphing $$2(3x+1) \leq 20$$ and $$4(x-1)

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Procedure for Solving Compound Inequalities with "and"

Example

Try It: Solving and Graphing $2(3x+1) \leq 20$ and $4(x-1) < 2$

To practice solving a compound inequality, solve $2(3x+1) \leq 20$ and $4(x-1) < 2$ . Solving the first inequality gives $6x + 2 \leq 20$ , which simplifies to $6x \leq 18$ or $x \leq 3$ . Solving the second inequality yields $4x - 4 < 2$ , which simplifies to $4x < 6$ or $x < \frac{3}{2}$ . Graphing both results shows that the intersection of $x \leq 3$ and $x < \frac{3}{2}$ is the interval where $x < \frac{3}{2}$ . In interval notation, this overlapping solution is written as $(-\infty, \frac{3}{2})$ .