Example

Try It: Solving and Graphing 5(3x1)105(3x-1) \leq 10 and 4(x+3)<84(x+3) < 8

To practice solving a compound inequality, solve 5(3x1)105(3x-1) \leq 10 and 4(x+3)<84(x+3) < 8. Solving the first inequality gives 15x51015x - 5 \leq 10, which simplifies to 15x1515x \leq 15 or x1x \leq 1. Solving the second inequality yields 4x+12<84x + 12 < 8, which simplifies to 4x<44x < -4 or x<1x < -1. Graphing both results shows that the intersection of x1x \leq 1 and x<1x < -1 is the interval where x<1x < -1. In interval notation, this overlapping solution is written as (,1)(-\infty, -1).

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Updated 2026-05-02

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