Question

1. solve \\(-4t - 5 > 2t + 13\\) for \\(t\\).

\\(t < -9\\)

\\(t > -3\\)

\\(t < -3\\)

\\(t > -9\\)

Explanation:

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<reasoning>

Isolate variable terms

Using the Linear Equation Solving and Algebraic Simplification knowledge points
\[

$$\begin{aligned} -4t - 5 &> 2t + 13 \\ -4t - 2t - 5 &> 13 \\ -6t - 5 &> 13 \end{aligned}$$

\]

Isolate constant terms

Using the Linear Equation Solving and Algebraic Simplification knowledge points
\[

$$\begin{aligned} -6t &> 13 + 5 \\ -6t &> 18 \end{aligned}$$

\]

Solve for t and reverse inequality sign

To solve for \(t\), we divide both sides by \(-6\). Since we are dividing by a negative number, we must reverse the inequality sign from \(>\) to \(<\).
\[

$$\begin{aligned} t &< \frac{18}{-6} \\ t &< -3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(t < -9\)</mcq-option>
<mcq-option>(B) \(t > -3\)</mcq-option>
<mcq-correct>(C) \(t < -3\)</mcq-correct>
<mcq-option>(D) \(t > -9\)</mcq-option>
</answer>

<plot>
{
"elements": [
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"type": "bentinequality",
"params": [{ "x": -3, "operator": "<", "labelText": " t < -3 " }],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3,
"showLabel": true
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Answer:

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<reasoning>

Isolate variable terms

Using the Linear Equation Solving and Algebraic Simplification knowledge points
\[

$$\begin{aligned} -4t - 5 &> 2t + 13 \\ -4t - 2t - 5 &> 13 \\ -6t - 5 &> 13 \end{aligned}$$

\]

Isolate constant terms

Using the Linear Equation Solving and Algebraic Simplification knowledge points
\[

$$\begin{aligned} -6t &> 13 + 5 \\ -6t &> 18 \end{aligned}$$

\]

Solve for t and reverse inequality sign

To solve for \(t\), we divide both sides by \(-6\). Since we are dividing by a negative number, we must reverse the inequality sign from \(>\) to \(<\).
\[

$$\begin{aligned} t &< \frac{18}{-6} \\ t &< -3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(t < -9\)</mcq-option>
<mcq-option>(B) \(t > -3\)</mcq-option>
<mcq-correct>(C) \(t < -3\)</mcq-correct>
<mcq-option>(D) \(t > -9\)</mcq-option>
</answer>

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"type": "bentinequality",
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