Question

question point q is on line segment $overline{pr}$. given $qr = 2x + 4, pq = x$, and $pr = 4x - 10$, determine the numerical length of $overline{pr}$. answer attempt 1 out of 2 $pr=$

Explanation:

Step1: Use segment - addition postulate

Since point Q is on line segment $\overline{PR}$, we have $PQ + QR=PR$. Substitute the given expressions: $x+(2x + 4)=4x-10$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+2x + 4=3x + 4$. So, $3x + 4=4x-10$.

Step3: Solve for x

Subtract $3x$ from both sides: $3x+4-3x=4x - 10-3x$, which gives $4=x - 10$. Then add 10 to both sides: $4 + 10=x-10 + 10$, so $x = 14$.

Step4: Find the length of PR

Substitute $x = 14$ into the expression for $PR$. Since $PR=4x-10$, then $PR=4\times14-10$. Calculate $4\times14-10=56 - 10=46$.

Answer:

$46$