Question

if:
ac = 53,
bc = 2x + 5, and
ab = 4x + 6,
find bc.

Explanation:

Step1: Use segment - addition postulate

Since $AC = AB + BC$, we substitute the given expressions: $53=(4x + 6)+(2x + 5)$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the right - hand side: $53 = 4x+2x + 6 + 5$, which simplifies to $53=6x + 11$.

Step3: Solve for $x$

Subtract 11 from both sides: $53−11 = 6x$, so $42 = 6x$. Then divide both sides by 6: $x=\frac{42}{6}=7$.

Step4: Find $BC$

Substitute $x = 7$ into the expression for $BC$. Since $BC = 2x+5$, then $BC=2\times7 + 5$.
$BC=14 + 5=19$.

Answer:

19