Let's define the length of the shorter section as \( x \) inches. Since one section of the string is 5 inches longer than the other, the length of the longer section can be expressed 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. This gives us the equation:
\[ 2(x + 5) = 3x \]
Now, let's solve this equation for \( x \):
-
Distribute the 2 on the left side: \[ 2x + 10 = 3x \]
-
Subtract \( 2x \) from both sides: \[ 10 = 3x - 2x \] \[ 10 = x \]
So, the length of the shorter section, \( x \), is 10 inches.
Answer: The shorter section is 10 inches long.