Question

Point F is on line segment \overline{EG} EG. Given FG=3x-5,EF=x, and EG=5x-8, determine the numerical length of \overline{FG}. FG.

Answer 1

x=3

FG=4

Step-by-step explanation

Step 1

Graph

now, make the equation

as you can see in the graph

`\begin{gathered} \text{yellow line=red line+ blue line} \\ \text{replacing} \\ EG=EF+FG \\ (5x-8)=x+(3x-5)\text{ Equation (1)} \end{gathered}`

Step 2

Solve the equation.

`\begin{gathered} (5x-8)=x+(3x-5)\text{ Equation (1)} \\ 5x-8=x+3x-5 \\ \text{add similar terms} \\ 5x-8=4x-5 \\ \text{subtract 4x in both sides} \\ 5x-8-4x=4x-5-4x \\ x-8=-5 \\ \text{ad 8 in both sides} \\ x-8+8=-5+8 \\ x=3 \end{gathered}`

Step 3

Finally, replace the value for x in FG

`\begin{gathered} FG=3x-5 \\ FG=3(3)-5 \\ FG=9-5 \\ FG=4 \end{gathered}`

I hope this helps you