Question

suppose Q is the midpoint of PR. Use the information to find the missing value. PR = 9x-31 and QR=43; find x

Answer 1

Answer:

x = 13

Step-by-step explanation:

If Q is the midpoint of PR...then

PR = 2QR...since QR is half the length of PR

;9x - 31 = 86

;9x = 86 + 31

;9x = 117

Hence x = 117/9 = 13

Answer 2

Suppose Q is the midpoint of PR and PR = 9x-31 and QR=43, then the value of x will be 13

The midpoint of a line is the point that bisects or divides the line into two equal parts.

Hence suppose Q is the midpoint of PR, then:

PQ + QR = PR .... 1

and PQ = QR ...... 2

Substitute equation 2 into 1:

QR + QR = PR

2QR = PR

Given that:

PR = 9x-31 and QR=43, then;

2(43) = 9x - 31

86 = 9x - 31

Swap

9x - 31 = 86

Add 31 to both sides

9x - 31 + 31 = 86 + 31

9x = 117

Divide both sides by 9

$\frac{9x}{9}= \frac{117}{9} \\x=13$

Hence the value of x is 13

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