Answer:
[tex]AC = 20[/tex]
Step-by-step explanation:
Given
[tex]AC = 2x + 8[/tex]
[tex]AB = 4x - 16[/tex]
[tex]BC = 3x - 6[/tex]
Required
Find AC
First, we need to solve for x
Since B is between A and C, then
[tex]AC = AB + BC[/tex]
Substitute values for AC, AB and BC
[tex]2x + 8 = 4x - 16 + 3x - 6[/tex]
Collect Like Terms
[tex]2x - 4x - 3x = -16 - 6 - 8[/tex]
[tex]-5x = -30[/tex]
Divide through by -5
[tex]\frac{-5x}{-5} = \frac{-30}{-5}[/tex]
[tex]x = \frac{-30}{-5}[/tex]
[tex]x = 6[/tex]
Substitute 6 for x in [tex]AC = 2x + 8[/tex]
[tex]AC= 2 * 6 + 8[/tex]
[tex]AC= 12 + 8[/tex]
[tex]AC = 20[/tex]
