To better understand the problem, let's make an illustration based on the information given.
Since F is the midpoint of segment EG, then the measure of EF is half the measure of EG.
[tex]6x+7=\frac{1}{2}(18x-4)[/tex]
From this, we can solve for x.
a. Multiply 1/2 by the terms inside the parenthesis.
[tex]6x+7=9x-2[/tex]
b. Subtract 6x on both sides of the equation.
[tex]6x-6x+7=9x-6x-2[/tex][tex]7=3x-2[/tex]
c. Add 2 on both sides of the equation.
[tex]7+2=3x-2+2[/tex][tex]9=3x[/tex]
d. Lastly, divide both sides of the equation by 3 to isolate the variable x.
[tex]\frac{9}{3}=\frac{3x}{3}[/tex][tex]3=x[/tex]
Answer:
Therefore, the value of x is 3.
