Question

which graph represents the solution of the inequality below?

(-1.2x - 6.5x \le 2.3x + 5)

Explanation:

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<reasoning>

Combine like terms on the left side

\[

$$\begin{aligned} -1.2x - 0.5x &\le 2.3x + 5 \\ -1.7x &\le 2.3x + 5 \end{aligned}$$

\]

Isolate the variable x

\[

$$\begin{aligned} -1.7x - 2.3x &\le 5 \\ -4x &\le 5 \end{aligned}$$

\]

Divide by -4 and reverse the inequality sign

\[

$$\begin{aligned} x &\ge \frac{5}{-4} \\ x &\ge -1.25 \end{aligned}$$

\]

The graph representing \(x \ge -1.25\) has a solid circle at \(-1.25\) (between \(-1\) and \(-2\), closer to \(-1\)) with an arrow pointing to the right. Looking at the options, the third graph has a solid circle at approximately \(-1.25\) with an arrow pointing to the right.
</reasoning>

<answer>
<mcq-option>(A) Solid circle at -0.5, arrow pointing left</mcq-option>
<mcq-option>(B) Solid circle at -2, arrow pointing left</mcq-option>
<mcq-correct>(C) Solid circle at -1.25, arrow pointing right</mcq-correct>
<mcq-option>(D) Solid circle at 2, arrow pointing right</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Combine like terms on the left side

\[

$$\begin{aligned} -1.2x - 0.5x &\le 2.3x + 5 \\ -1.7x &\le 2.3x + 5 \end{aligned}$$

\]

Isolate the variable x

\[

$$\begin{aligned} -1.7x - 2.3x &\le 5 \\ -4x &\le 5 \end{aligned}$$

\]

Divide by -4 and reverse the inequality sign

\[

$$\begin{aligned} x &\ge \frac{5}{-4} \\ x &\ge -1.25 \end{aligned}$$

\]

The graph representing \(x \ge -1.25\) has a solid circle at \(-1.25\) (between \(-1\) and \(-2\), closer to \(-1\)) with an arrow pointing to the right. Looking at the options, the third graph has a solid circle at approximately \(-1.25\) with an arrow pointing to the right.
</reasoning>

<answer>
<mcq-option>(A) Solid circle at -0.5, arrow pointing left</mcq-option>
<mcq-option>(B) Solid circle at -2, arrow pointing left</mcq-option>
<mcq-correct>(C) Solid circle at -1.25, arrow pointing right</mcq-correct>
<mcq-option>(D) Solid circle at 2, arrow pointing right</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
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