Question

write a simplified expression for the length of $overline{ac}$. a $x + 2$ b $7x - 3$ c ac = □ write a simplified expression for the length of $overline{qr}$. p $8y+5$ q $13y + 25$ r qr = □

Explanation:

Step1: Find length of AC

Since $AC = AB + BC$, and $AB=x + 2$, $BC = 7x-3$, then $AC=(x + 2)+(7x-3)$.

Step2: Simplify the expression for AC

Combine like - terms: $(x+7x)+(2 - 3)=8x-1$.

Step3: Find length of QR

Since $QR=PR - PQ$, and $PR = 13y + 25$, $PQ=8y + 5$, then $QR=(13y + 25)-(8y + 5)$.

Step4: Simplify the expression for QR

Distribute the negative sign: $13y+25 - 8y-5$. Then combine like - terms: $(13y-8y)+(25 - 5)=5y + 20$.

Answer:

$AC = 8x-1$
$QR=5y + 20$