Question

Which value of x would make NO || Kj?

K
(x + 2) in.
N
оооо
(x - 3) in
8
L
(x-4) in. O
xin.
J

Answer 1

`x = 8`

Explanation:

Given

The attached figure

Required

Find x

To find x, we make use of the following equivalent ratios:

`LN : LO = NK:OJ`

This gives:

`(x-3) : (x - 4) = (x +2) : (x)`

Convert to fractions

`(x-3)/(x-4) = (x+2)/(x)`

Cross Multiply

`x(x-3) = (x-4)(x+2)`

Open brackets

`x^2-3x = x^2 -4x +2x - 8`

Collect Like Terms

`x^2 - x^2-3x +4x -2x =- 8`

`-3x +4x -2x =- 8`

`-1x =- 8`

`-x =- 8`

Multiply through by -1

`-1 * -x =- 8*-1`

`x = 8`