Question

5x + 13 and 10x - 7 represent the lengths in inches of 2 sides of an equilateral octagon. What is the length of one side

Answer 1

Step-by-step explanation

Step 1

an equilateral octagon has all same equals, it means both measures are equal

`5x+3=10x-7\text{ }`

Step 2

Solve for x

i)subtract 5x in both sides

`\begin{gathered} 5x+3=10x-7 \\ 5x+3-5x=10x-7-5x \\ 3=5x-7 \end{gathered}`

ii) add 7 in both sides

`\begin{gathered} 3=5x-7 \\ 3+7=5x-7+7 \\ 10=5x \end{gathered}`

iii)finally, divide each side by 5

`\begin{gathered} 10=5x \\ (10)/(5)=(5x)/(5) \\ x=2 \end{gathered}`

Step 3

to know the length of one side, just replace the value for x

`\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}`