Explanation
Step 1
an equilateral octagon has all same equals, it means both measures are equal
[tex]5x+3=10x-7\text{ }[/tex]Step 2
Solve for x
i)subtract 5x in both sides
[tex]\begin{gathered} 5x+3=10x-7 \\ 5x+3-5x=10x-7-5x \\ 3=5x-7 \end{gathered}[/tex]ii) add 7 in both sides
[tex]\begin{gathered} 3=5x-7 \\ 3+7=5x-7+7 \\ 10=5x \end{gathered}[/tex]iii)finally, divide each side by 5
[tex]\begin{gathered} 10=5x \\ \frac{10}{5}=\frac{5x}{5} \\ x=2 \end{gathered}[/tex]Step 3
to know the length of one side, just replace the value for x
[tex]\begin{gathered} \text{length of one side= 5x+13} \\ \text{length of one side= 5}\cdot2\text{+13} \\ \text{length of one side= 10+13} \\ \text{length of one side= 2}3 \end{gathered}[/tex]