To solve the inequality \(-2(-10x + 7) \leq 8\), follow these steps:
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Distribute \(-2\) on the left side: \[ -2 \cdot -10x + (-2) \cdot 7 \leq 8 \] This simplifies to: \[ 20x - 14 \leq 8 \]
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Next, add \(14\) to both sides to isolate the term with \(x\): \[ 20x - 14 + 14 \leq 8 + 14 \] This simplifies to: \[ 20x \leq 22 \]
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Finally, divide both sides by \(20\) to solve for \(x\): \[ x \leq \frac{22}{20} \] Simplifying the fraction gives: \[ x \leq \frac{11}{10} \] or: \[ x \leq 1.1 \]
Thus, the solution to the inequality is: \[ x \leq 1.1 \]
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