Answer:
[tex]x = 8[/tex]
Step-by-step explanation:
Given
The attached figure
Required
Find x
To find x, we make use of the following equivalent ratios:
[tex]LN : LO = NK:OJ[/tex]
This gives:
[tex](x-3) : (x - 4) = (x +2) : (x)[/tex]
Convert to fractions
[tex]\frac{x-3}{x-4} = \frac{x+2}{x}[/tex]
Cross Multiply
[tex]x(x-3) = (x-4)(x+2)[/tex]
Open brackets
[tex]x^2-3x = x^2 -4x +2x - 8[/tex]
Collect Like Terms
[tex]x^2 - x^2-3x +4x -2x =- 8[/tex]
[tex]-3x +4x -2x =- 8[/tex]
[tex]-1x =- 8[/tex]
[tex]-x =- 8[/tex]
Multiply through by -1
[tex]-1 * -x =- 8*-1[/tex]
[tex]x = 8[/tex]
