To solve the inequality \( \frac{3}{4}x - 10 \leq 2 \), follow these steps:
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Add 10 to both sides: \[ \frac{3}{4}x - 10 + 10 \leq 2 + 10 \] \[ \frac{3}{4}x \leq 12 \]
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Multiply both sides by \(\frac{4}{3}\) to isolate \(x\). Note that since \(\frac{4}{3}\) is positive, the direction of the inequality does not change: \[ x \leq 12 \cdot \frac{4}{3} \] \[ x \leq 16 \]
Thus, the solution to the inequality is: \[ x \leq 16 \]
In interval notation, the solution is: \[ (-\infty, 16] \]