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QuestionFind xx given that QQ is the midpoint of segment PRPR, QR=18QR=18, and PR=5x+6PR=5x+6.

Studdy Solution

STEP 1

Assumptions1. Point Q is the midpoint of Segment PR. . QR =183. PR =5x +64. Since Q is the midpoint of PR, PQ = QR.

STEP 2

We know that PQ = QR. So, we can set up the equationQ=QRQ = QR

STEP 3

Substitute the given values into the equationQ=18Q =18

STEP 4

Since Q is the midpoint of PR, the length of segment PR is twice the length of either segment PQ or QR. So, we can set up the equationPR=2⋅PQPR =2 \cdot PQ

STEP 5

Substitute the given values into the equation5x+=2⋅185x + =2 \cdot18

STEP 6

implify the right side of the equation5x+6=365x +6 =36

STEP 7

Subtract6 from both sides of the equation to isolate the term with x5x=36−65x =36 -6

STEP 8

implify the right side of the equation5x=305x =30

STEP 9

Divide both sides of the equation by5 to solve for xx=305x = \frac{30}{5}

STEP 10

implify the right side of the equation to find the value of xx=6x =6The value of x is6.

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