Question

Point B is on line segment AC

. Given AB=4x-6,AB=4x−6, AC=2x+10,AC=2x+10, and BC=4,BC=4, determine the numerical length of AC

Answer 1

22

Explanation:

We are looking at a line that has been cut, so we have 2 lines that add up to 1. It is represented as AB + BC = AC. Let's plug in the lines and solve.

AB + BC = AC
(4x - 6) + (4) = 2x + 10 Original equation
4x - 2 = 2x + 10 Simplified equation
4x = 2x + 12 Add 2 to both sides
2x = 12 Subtract 2x from both sides
x = 6 Divide both sides by 2

Now we know that x equals 6. Let's plug it into the line to find AC.

2(6) + 10
12 + 10
22

The numerical length of AC is 22.