Question

I need to show work..

Answer 1

Explanation:

Since the two sides of the triangle are equal and (it appears) the angle
`D` is bisected by
`DG`, then we can say that
`EG` and
`GF` are equivalent.

Knowing this, we can set the two lines equal to each other and solve for
`x`:

`2x + 11 = 14x - 37`

`2x - 14x = -37 - 11`

`-12x = -48`

`x = 4`

Since we need to find
`EG`, we need to plug in
`x = 4` into its equation:

`2x + 11`

`2(4) + 11`

`8 + 11`

`19`

Answer 2

`2x + 11 = 14x - 37 \\11 + 37 = 14x - 2x \\ 48 = 12x \\ (48)/(12) = (12x)/(12) \\ 4 = x`

now let's find the value of EG

`eg = 2x + 11 \\ x = 4 \\ \\ 2x + 11 \\ 2 * 4 + 11 \\ 8 + 11 \\ = 19`