Question

Point B is on line segment overline AC. Given AB=4x-6 AC=2x+10 , and BC=4 , determine the numerical length of overline AC Answer: AC=□

Answer 1

To find the length of overline AC, we use the Segment Addition Postulate, which gives us an equation to solve for x. Upon finding x, we substitute it back into the expression for AC to find that the numerical length of overline AC is 22.

Step-by-step explanation:

To determine the numerical length of overline AC, we need to use the given information that Point B is on line segment overline AC with AB=4x-6, AC=2x+10, and BC=4. Since B lies on segment AC, by the Segment Addition Postulate, AB + BC = AC. By substituting the given values in, we get:

1. 4x - 6 (the length of AB) + BC (which is given as 4) = 2x + 10 (the length of AC).
2. Solve for x: 4x - 6 + 4 = 2x + 10.
3. 4x - 2 + 4 = 2x + 10.
4. Simplify the equation: 2x = 12.
5. Divide both sides by 2: x = 6.

Now plug the value of x back into the expression for AC:

• AC = 2x + 10 = 2(6) + 10 = 12 + 10.
• Therefore, the length of overline AC is 22.