Question

solve the inequality below for x.

\\-3.2(2x - 1) \le 17.6\\

\\(x \ge -2.25\\)
\\(x \le -2.25\\)
\\(x \ge 10.9\\)
\\(x \le 10.9\\)

Explanation:

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<reasoning>

Divide both sides by the negative coefficient

\[

$$\begin{aligned} -3.2(2x - 1) &\le 17.6 \\ 2x - 1 &\ge \frac{17.6}{-3.2} \\ 2x - 1 &\ge -5.5 \end{aligned}$$

\]

Isolate the variable term

\[

$$\begin{aligned} 2x &\ge -5.5 + 1 \\ 2x &\ge -4.5 \end{aligned}$$

\]

Solve for x

\[

$$\begin{aligned} x &\ge \frac{-4.5}{2} \\ x &\ge -2.25 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x \ge -2.25\)</mcq-correct>
<mcq-option>(B) \(x \le -2.25\)</mcq-option>
<mcq-option>(C) \(x \ge 10.9\)</mcq-option>
<mcq-option>(D) \(x \le 10.9\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Divide both sides by the negative coefficient

\[

$$\begin{aligned} -3.2(2x - 1) &\le 17.6 \\ 2x - 1 &\ge \frac{17.6}{-3.2} \\ 2x - 1 &\ge -5.5 \end{aligned}$$

\]

Isolate the variable term

\[

$$\begin{aligned} 2x &\ge -5.5 + 1 \\ 2x &\ge -4.5 \end{aligned}$$

\]

Solve for x

\[

$$\begin{aligned} x &\ge \frac{-4.5}{2} \\ x &\ge -2.25 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x \ge -2.25\)</mcq-correct>
<mcq-option>(B) \(x \le -2.25\)</mcq-option>
<mcq-option>(C) \(x \ge 10.9\)</mcq-option>
<mcq-option>(D) \(x \le 10.9\)</mcq-option>
</answer>

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