Let's define the length of the shorter section as \( x \) inches. According to the problem, the longer section is 5 inches longer than the shorter section, so we can express the longer section's length as \( x + 5 \) inches.
The problem states that twice the length of the longer section is equal to three times the length of the shorter section. This can be written as the following equation:
\[ 2(x + 5) = 3x \]
Now, let's solve this equation for \( x \):
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Expand the left side: \[ 2x + 10 = 3x \]
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Subtract \( 2x \) from both sides: \[ 10 = 3x - 2x \] \[ 10 = x \]
Thus, the length of the shorter section is \( 10 \) inches.
So, the answer is 10 inches.
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