If line y bisects ac, ab =4-5x, and bc =2x+25, find ac

The value of AC= 38

Given :

If line y bisects AC, AB =4-5x, and BC =2x+25

The graph is attached below

Explanation :

WE know that line y bisects AC. So we can say that AB=BC

Now we replace AB  and BC  to solve for x

Using value of x we find out AC

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If B is a midpoint between points A and C, then AC = AB + BC and AB = BC.

AB = 4 - 5x, BC = 2x + 25

substitute

4 - 5x = 2x + 25 |-4

-5x = 2x + 21 |-2x

-7x = 21 |:(-7)

x = -3

AB = BC → AC = 2AB = 2BC

BC = 2x + 25 → BC = 2(-3) + 25 = -6 + 25 = 19

AC = 2(19) = 38

AC = 38

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