QuestionAugust 24, 2025

Point Q is on line segment overline (PR) Given QR=3x,PQ=x+6 and PR=5x-4 determine the numerical length of overline (PQ) Answer Attempt1out of 2 PQ=square

Point Q is on line segment overline (PR) Given QR=3x,PQ=x+6 and PR=5x-4 determine the numerical length of overline (PQ) Answer Attempt1out of 2 PQ=square
Point Q is on line segment overline (PR) Given QR=3x,PQ=x+6 and PR=5x-4
determine the numerical length of overline (PQ)
Answer Attempt1out of 2
PQ=square

Solution
4.5(146 votes)

Answer

16 Explanation 1. Set up the equation Since Q is on \overline{PR}, we have PQ + QR = PR. Substitute the given expressions: (x + 6) + 3x = 5x - 4. 2. Simplify and solve for x Combine like terms: 4x + 6 = 5x - 4. Rearrange to find x: 6 + 4 = 5x - 4x, so x = 10. 3. Calculate PQ Substitute x = 10 into PQ = x + 6: PQ = 10 + 6 = 16.

Explanation

1. Set up the equation<br /> Since $Q$ is on $\overline{PR}$, we have $PQ + QR = PR$. Substitute the given expressions: $(x + 6) + 3x = 5x - 4$.<br />2. Simplify and solve for $x$<br /> Combine like terms: $4x + 6 = 5x - 4$. Rearrange to find $x$: $6 + 4 = 5x - 4x$, so $x = 10$.<br />3. Calculate $PQ$<br /> Substitute $x = 10$ into $PQ = x + 6$: $PQ = 10 + 6 = 16$.
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