Question

if: ac = 26, bc = 7x + 2, and ab = 9x + 8, find bc.

Explanation:

Step1: Use segment - addition postulate

Since $AC = AB+BC$, we substitute the given expressions: $26=(9x + 8)+(7x + 2)$.

Step2: Combine like - terms

$26=9x+7x + 8 + 2$, which simplifies to $26 = 16x+10$.

Step3: Solve for $x$

Subtract 10 from both sides: $26−10=16x$, so $16 = 16x$. Then divide both sides by 16, getting $x = 1$.

Step4: Find $BC$

Substitute $x = 1$ into the expression for $BC$. Since $BC=7x + 2$, then $BC=7\times1+2$.
$BC=7 + 2=9$.

Answer:

$9$