R is the midpoint of line segment of PQ. PR is 3x + 6 and RQ is 5x - 2.Find the followingX:PR:RO:PQ:

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EvalynW606583 EvalynW606583 · Answer 1 · 2022-10-31T08:05:56+01:00

Let's draw a diagram to represent the given problem.

If R is midpoint then PR and RQ are equal by definition of midpoint. So, we can express the following equation.

[tex]\begin{gathered} PR=RQ \\ 3x+6=5x-2 \end{gathered}[/tex]

Then, we solve for x. First, we subtract 5x on each side.

[tex]\begin{gathered} 3x-5x+6=5x-5x-2 \\ -2x+6=-2 \end{gathered}[/tex]

Now, we subtract 6 on each side.

[tex]\begin{gathered} -2x+6-6=-2-6 \\ -2x=-8 \end{gathered}[/tex]

At last, we divide the equation by -2.

[tex]\begin{gathered} \frac{-2x}{-2}=\frac{-8}{-2} \\ x=4 \end{gathered}[/tex]

We use this value to find PR and RQ.

[tex]PR=3x+6=3(4)+6=12+6=18=RQ[/tex]

Then, we find PQ.

[tex]PQ=18+18=36[/tex]