Let's denote the length of the shorter section as \( x \) inches. Since the longer section is 5 inches longer than the shorter section, we can express the length of the longer section as \( x + 5 \) inches.
According to the problem, twice the length of the longer section is equal to three times the length of the shorter section. We can write this as an equation:
\[ 2(x + 5) = 3x \]
Now, let's solve for \( x \):
- Expand the left side:
\[ 2x + 10 = 3x \]
- Subtract \( 2x \) from both sides:
\[ 10 = 3x - 2x \]
- This simplifies to:
\[ 10 = x \]
So, the length of the shorter section is \( \boxed{10} \) inches.
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