What is the solution set for the inequality –8(x + 3) ≤ 2(–2x + 10)?

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Accepted Answer

First, multiply (x + 3) by –8 and multiply (–2x + 10) by 2: –8(x + 3) = –8x – 24, 2(–2x + 10) = –4x + 20. Then, add 8x to both sides of the inequality and subtract 20 from both sides of the inequality: –8x – 24 ≤ –4x + 20 –8x – 24 + 8x ≤ –4x + 20 + 8x –24 ≤ 4x + 20 –24 – 20 ≤ 4x + 20 – 20 –44 ≤ 4x Finally, divide both sides of the inequality by 4: –44 ⁄ 4 ≤ 4x ⁄ 4 , x ≥ –11.

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