In the diagram below of triangle EFG, H is a midpoint of EF and J is a midpoint of FG. If H J = 4x + 6, and EG = 34 - 3x, what is the measure of H J?

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Step-by-step explanation:  2(4x+6)=

\,\,34-3x

34−3x

Since HJ is a midsegment, twice HJ is equal to EG.

8x+12=

8x+12=

\,\,34-3x

34−3x

Distribute.

8x+12=

8x+12=

\,\,-3x+34

−3x+34

Communicative property to change the order

\color{red}{+3x}\phantom{+12}\phantom{=}

+3x+12=

\,\,\color{red}{+3x}\phantom{+34}

+3x+34

+3x to both sides.

11x+12=

11x+12=

\,\,34

34

\phantom{11x}\color{red}{-12}\phantom{=}

11x−12=

\,\,\color{red}{-12}

−12

-12 to both sides.

11x=

11x=

\,\,22

22

\frac{11x}{11}=

11

11x

​  

=

\,\,\frac{22}{11}

11

22

​  

Divide both sides by 11

x=

x=

\,\,2

2

Value of x

HJ=

HJ=

\,\,4x+6

4x+6

Value of HJ

HJ=

HJ=

\,\,4(2)+6

4(2)+6

Plug in x.

HJ=

HJ=

\,\,8+6

8+6

Multiply.

HJ=

HJ=

\,\,14

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