Step 1
Total length = 50 inches
Let the length of the first piece = x
The length of the second piece = x - 10
Step 2:
[tex]\begin{gathered} \text{Total length = 50} \\ x\text{ + x - 10 = 50} \\ 2x\text{ = 50 + 10} \\ 2x\text{ = 60} \\ x\text{ = 30 inches} \end{gathered}[/tex]Final answer
Length of the shorter piece = x - 10
= 30 - 10 = 20 inches