Let's begin by listing out the information given to us:
[tex]\begin{gathered} |P|=2x+50 \\ |Q|=5x-10 \end{gathered}[/tex]
|P| & |Q| are parallel lines: |P| = |Q|
Since |P| & |Q| are parallel lines, we equate both of them to solve for x, we have:
[tex]\begin{gathered} |P|=|Q| \\ 2x+50=5x-10 \\ \text{Put like terms together} \\ \text{Subtract 2x from both side, we have:} \\ 2x-2x+50=5x-2x-10 \\ 50=3x-10 \\ \text{Add 10 to both sides} \\ 50+10=3x-10+10 \\ 60=3x\Rightarrow3x=60 \\ \text{Divide both side by 3, we have:} \\ \frac{3}{3}x=\frac{60}{3}\Rightarrow x=20 \\ x=20 \end{gathered}[/tex]
