Question

question point q is on line segment pr. given qr = 2x + 4, pq = x, and pr = 4x - 10, determine the numerical length of pr. answer pr =

Explanation:

Step1: Use segment - addition postulate

Since point Q is on line segment $\overline{PR}$, we know that $PQ + QR=PR$.
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: $3x+4-3x=4x - 10-3x$.
We get $4=x - 10$.
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 $PR$.
$PR=4x-10=4\times14-10$.
$PR = 56-10=46$.

Answer:

$46$