Question

Point F is on line segment EG given EG=5x + 7, EF=5x, and FG=2x - 7, determine the numerical length of FG

Answer 1

`FG = 7`

Explanation:

Given

`EG = 5x + 7`

`EF = 5x`

`FG = 2x - 7`

Required

Determine the length of FG

Since, F is on segment EG, then

`EG= EF + FG`

Substitute values for EG, EF and FG

`5x + 7 = 5x + 2x - 7`

Collect Like Terms

`5x - 5x - 2x = -7 - 7`

`- 2x = -14`

Solve for x

`x = -14/-2`

`x = 7`

Substitute 7 for x in
`FG = 2x - 7`

`FG = 2 * 7- 7`

`FG = 14- 7`

`FG = 7`