Help please and thank you!

Question

A line segment AC is bisected by point B. The length OF AB is 8x+12 and the length of BC is 6x+18.

A. What is the value of x?

B. What is the length of AB?

C. What is the length of AC?

Answer 1

When a line is bisected, that means that both sides are equal. Ex. If a line of length 10 is bisected, then each segment is 5.

8x+12 6x+18

•---------------|--------------•

A B C

By definition the length of AB = the length of BC therefore

AB = BC

8x+12 = 6x+18

a) What is the value of x?

8x+12 = 6x+18 Solve for x, put like-variables on the same side

8x-6x = 18-12 Simplify

2x = 6 Divide both sides by 2

x = 3

b) What is the length of AB?

We found that x = 3 and given that AB = 8x+12, we plug x into that equation.

AB = 8x + 12

AB = 8(3) + 12

AB = 24 + 12

AB = 36

c) What is the length of AC?

Since the line is bisected, AB = BC, so you can double AB to get the answer 2(AB) = 2(36) = 72

Or you can solve for BC using x and add the two together to make sure your equations are correct.

BC = 6x+18

BC = 6(3) + 18

BC = 18 + 18

BC = 36

AC = AB + BC

AC = 36 + 36

AC = 72