8. If BD BC, BD = 5x - 26, BC = 2x + 1, and AC = 43, find AB.

AB is 24

Step-by-step explanation:

Using the segment addition postulate, AC = AB+BC.

We know that BD=BC, BD=5x-26 and BC=2x+1. So set up an equation to find the value of x:

5x-26=2x+1

Subtract 2x from each side:

5x-26-2x = 2x+1-2x

3x-26 = 1

Add 26 to each side:

3x-26+26 = 1+26

3x=27

Divide both sides by 3:

3x/3 = 27/3

x = 9

This means that BC = 2x+1 = 2 (9) + 1 = 18+1 = 19.

We know that AC = AB+BC; using our given information as well as the value of BC we just found, we have

43 = AB+19

Subtract 19 from each side:

43-19 = AB+19-19

24 = AB