Question

Point B is on line segment AC. Given AB = 4x – 6, AC = 2x + 10, and
BC = 4, determine the numerical length of AC.
Answer: AC =
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attempt 1 out of 2
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Answer 1

Answer:

AC=22

Step-by-step explanation:

If point B in somewhere along a segment between the points A and C, then it means that AB + BC = AC.

A---------------------------------C

A------------B-------------------C

     AB      +        BC       = AC

This means that we can write an equation:

4x-6(AB) + 4(BC) = 2x+10 (AC)

Which we can now solve for x:

(4x-6)+4=2x+10

Take out of brackets:

4x-6+4=2x+10

Combine like terms:

4x-2=2x+10

Move x terms to one side and other terms to the other:

4x-2x=10+2

Combine:

2x=12

Solve:

x=6

Now we can just substitute the x into the original AC equation to find its numerical length:

AC=2x+10

AC=2(6)+10

AC=12+10

AC=22

Hope this helped!