Question

What is the mid point of 3x+38 and 7x-16

Answer 1

Let:

A = 3x + 38

B = 7x - 16

C = the midpoint of A and B

`\begin{gathered} A=B \\ so\colon \\ 3x+38=7x-16 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 38+16=7x-3x \\ 54=4x \\ x=(54)/(4) \\ x=13.5 \end{gathered}`

so:

`\begin{gathered} C=(A+B)/(2) \\ C=(3x+38+7x-16)/(2) \\ C=(3(13.5)+38+7(13.5)-16)/(2) \\ C=(157)/(2) \\ C=78.5 \end{gathered}`