Example

Try It: Solving and Graphing 2(3x+1)202(3x+1) \leq 20 and 4(x1)<24(x-1) < 2

To practice solving a compound inequality, solve 2(3x+1)202(3x+1) \leq 20 and 4(x1)<24(x-1) < 2. Solving the first inequality gives 6x+2206x + 2 \leq 20, which simplifies to 6x186x \leq 18 or x3x \leq 3. Solving the second inequality yields 4x4<24x - 4 < 2, which simplifies to 4x<64x < 6 or x<32x < \frac{3}{2}. Graphing both results shows that the intersection of x3x \leq 3 and x<32x < \frac{3}{2} is the interval where x<32x < \frac{3}{2}. In interval notation, this overlapping solution is written as (,32)(-\infty, \frac{3}{2}).

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Updated 2026-05-02

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