Question

solve the equation for \\(x\\) from todays warm up, \\(3x + 2 = x + 5\\), and find the weight of the square.

a the square weighs \\(\frac{3}{2}\\).
b the square weighs \\(\frac{7}{2}\\).
c the square weighs \\(\frac{2}{3}\\).
d the square weighs 2.

Explanation:

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<reasoning>

Identify the given equation

The problem asks us to solve the equation \(3x + 2 = x + 5\), which represents the balanced scale shown in the image.

Subtract x from both sides

To group the variable terms, we subtract \(x\) from both sides of the equation:
\[
(3x - x) + 2 = 5
\]
\[
2x + 2 = 5
\]

Subtract 2 from both sides

To isolate the variable term, we subtract \(2\) from both sides:
\[
2x = 5 - 2
\]
\[
2x = 3
\]

Solve for x

To find the value of \(x\), which represents the weight of the square, we divide both sides by \(2\):
\[
x = \frac{3}{2}
\]

Match with the options

The weight of the square is \(x = \frac{3}{2}\). This matches option B: "The square weighs \(\frac{3}{2}\)."
</reasoning>

<answer>
<mcq-option>(A) The square weighs \(\frac{2}{3}\).</mcq-option>
<mcq-correct>(B) The square weighs \(\frac{3}{2}\).</mcq-correct>
<mcq-option>(C) The square weighs \(\frac{7}{2}\).</mcq-option>
<mcq-option>(D) The square weighs 2.</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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Answer:

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</pre_analysis>

<reasoning>

Identify the given equation

The problem asks us to solve the equation \(3x + 2 = x + 5\), which represents the balanced scale shown in the image.

Subtract x from both sides

To group the variable terms, we subtract \(x\) from both sides of the equation:
\[
(3x - x) + 2 = 5
\]
\[
2x + 2 = 5
\]

Subtract 2 from both sides

To isolate the variable term, we subtract \(2\) from both sides:
\[
2x = 5 - 2
\]
\[
2x = 3
\]

Solve for x

To find the value of \(x\), which represents the weight of the square, we divide both sides by \(2\):
\[
x = \frac{3}{2}
\]

Match with the options

The weight of the square is \(x = \frac{3}{2}\). This matches option B: "The square weighs \(\frac{3}{2}\)."
</reasoning>

<answer>
<mcq-option>(A) The square weighs \(\frac{2}{3}\).</mcq-option>
<mcq-correct>(B) The square weighs \(\frac{3}{2}\).</mcq-correct>
<mcq-option>(C) The square weighs \(\frac{7}{2}\).</mcq-option>
<mcq-option>(D) The square weighs 2.</mcq-option>
</answer>

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