To solve the inequality \((1/2)x + 6 \leq -11\), we will first isolate \(x\).
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Subtract 6 from both sides: \[ \frac{1}{2}x + 6 - 6 \leq -11 - 6 \] Which simplifies to: \[ \frac{1}{2}x \leq -17 \]
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Next, multiply both sides by 2 to eliminate the fraction: \[ 2 \cdot \frac{1}{2}x \leq 2 \cdot -17 \] This gives us: \[ x \leq -34 \]
So, the solution to the inequality is \(x \leq -34\).
From the options given:
- \(x \leq -34\) is correct.
- \(x \geq -34\) is incorrect.
- \(x < -17\) is also incorrect.
The correct response is \(x \leq -34\).
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