Question

pq = 2x - 3. if qr = 5x + 7 and pr = 10x - 11, then pr =?

Explanation:

Step1: Use segment - addition postulate

Since $PR = PQ+QR$, we substitute the given expressions: $10x - 11=(2x - 3)+(5x + 7)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(2x - 3)+(5x + 7)=2x-3 + 5x+7=7x + 4$. So, $10x - 11=7x + 4$.

Step3: Solve for x

Subtract $7x$ from both sides: $10x-7x - 11=7x-7x + 4$, which gives $3x-11 = 4$. Then add 11 to both sides: $3x-11 + 11=4 + 11$, so $3x=15$. Divide both sides by 3: $x = 5$.

Step4: Find the value of PR

Substitute $x = 5$ into the expression for $PR$: $PR=10x - 11=10\times5-11=50 - 11=39$.

Answer:

39