Example

Try It: Solving and Graphing 25x32 - 5x \leq -3 or 5+2x35 + 2x \leq 3

To practice solving another compound inequality connected by 'or', evaluate 25x32 - 5x \leq -3 or 5+2x35 + 2x \leq 3. For the first inequality, subtracting 2 yields 5x5-5x \leq -5, and dividing by -5 (reversing the inequality sign) gives x1x \geq 1. For the second inequality, subtracting 5 yields 2x22x \leq -2, and dividing by 2 gives x1x \leq -1. Graphing both results demonstrates that the union consists of two distinct intervals: numbers less than or equal to -1 and numbers greater than or equal to 1. In interval notation, this combined solution is written as (,1][1,)(-\infty, -1] \cup [1, \infty).

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Updated 2026-05-02

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