To solve the inequality \(-30 + 5x \leq 4(8x + 6)\), we can follow these steps:
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Distribute on the right side: \[ 4(8x + 6) = 32x + 24 \] So the inequality becomes: \[ -30 + 5x \leq 32x + 24 \]
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Move all terms involving \(x\) to one side and constant terms to the other side. We can subtract \(5x\) from both sides: \[ -30 \leq 32x - 5x + 24 \] This simplifies to: \[ -30 \leq 27x + 24 \]
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Next, subtract 24 from both sides: \[ -30 - 24 \leq 27x \] Which simplifies to: \[ -54 \leq 27x \]
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Now divide both sides by 27: \[ \frac{-54}{27} \leq x \] Simplifying \(\frac{-54}{27}\): \[ -2 \leq x \]
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This can be rewritten as: \[ x \geq -2 \]
Therefore, the solution to the inequality is: \[ x \geq -2 \]
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