Question

If EF = 4x − 16, FG = 3x − 6, and EG = 27, find the values of x, EF, and FG.

Answer 1

EF + FG = EG
2x-12+3x-15=23
5x=50
x=10

EF=2(10)-12=8

FG=3(10)-15=15

Answer 2

By the segment addition postulate:

If F is on segment EG, then
`EF+FG = EG`

As per the statement:

If EF = 4x − 16, FG = 3x − 6, and EG = 27

then by above definition we have;

`EF+FG = EG`

`4x-16+3x-6 = 27`

Combine like terms;

`7x-22= 27`

Add 22 to both sides we have;

`7x=49`

Divide both sides by 7 we have;

x = 7

EF = 4x-16 = 4(7)-16 = 28-16 = 12

FG = 3x-6 = 3(7)-6 = 21-6 = 15

Therefore, the values are x = 7, EF = 12 and FG = 15.