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 attempt 1 out of 2 ac = _ this is the only question in this section. segment addition / subtraction (algebra)

Explanation:

Step1: Use segment - addition postulate

Since point B is on line - segment AC, we know that \(AB + BC=AC\). Given \(AB = 4x - 6\), \(AC = 2x+16\), and \(BC = 4\), we substitute these values into the equation: \((4x - 6)+4=2x + 16\).

Step2: Simplify the left - hand side of the equation

Combine like terms on the left - hand side: \(4x-6 + 4=4x-2\). So the equation becomes \(4x-2=2x + 16\).

Step3: Isolate the variable terms

Subtract \(2x\) from both sides of the equation: \(4x-2x-2=2x-2x + 16\), which simplifies to \(2x-2=16\).

Step4: Solve for x

Add 2 to both sides: \(2x-2 + 2=16+2\), so \(2x=18\). Then divide both sides by 2: \(x = 9\).

Step5: Find the length of AC

Substitute \(x = 9\) into the expression for AC. \(AC=2x + 16\), so \(AC=2\times9+16\). First, calculate \(2\times9 = 18\), then \(18+16=34\).

Answer:

34