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In this question, it is given that

P is the midpoint of line XY, XP=8x-2, and PY= 12x-30.

And if P is the midpoint of XY, then it divided XY in two equal part, that is XP and

PY.

So we have

[tex] XP = PY  \\ 8x-2 = 12x-30  \\ -2 + 30 = 12x-8x \\ 4x = 28 \\ x=7 [/tex]

Answer:

x=7

Step-by-step explanation:

P is the midpoint of line XY

Midpoint divides the line equally into two equal lines

So XP= PY

XP=8x-2, and PY= 12x-30

[tex]8x-2= 12x-30[/tex]

Solve the equation for x

[tex]8x-2= 12x-30[/tex]

Subtract 8x form both sides

[tex]-2= 4x-30[/tex]

Now we add 30 on both sides

[tex]28= 4x[/tex]

Divide both sides by 4

x=7

The value of x=7

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