Question

point b is on line segment $overline{ac}$. given $ab = 2x + 10$, $bc = x$, and $ac = 5x$, determine the numerical length of $overline{ac}$.

Explanation:

Step1: Use segment - addition postulate

Since point B is on line - segment $\overline{AC}$, we know that $AB + BC=AC$. Substitute the given expressions: $(2x + 10)+x = 5x$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+x + 10=5x$, which simplifies to $3x + 10=5x$.

Step3: Solve for x

Subtract $3x$ from both sides of the equation: $3x+10−3x = 5x−3x$. This gives $10 = 2x$. Then divide both sides by 2: $x=\frac{10}{2}=5$.

Step4: Find the length of AC

We know that $AC = 5x$. Substitute $x = 5$ into the expression for $AC$: $AC=5\times5 = 25$.

Answer:

$25$