Answer:
[tex]x=\frac{8}{3}=2\frac{2}{3}\approx{2.667}[/tex]
Step-by-step explanation:
[tex]\overline{PG}=2x+3\\\overline{GQ}=5x-5[/tex]
Since they're equidistant (equal distances), we can set them equal to one another and solve for x:
[tex]2x+3=5x-5[/tex]
Adding 5 to both sides:
[tex]2x+8=5x[/tex]
Subtracting 2x from both sides:
[tex]8=3x[/tex]
Dividing both sides by 3:
[tex]\frac{8}{3}=x[/tex]
Therefore:
[tex]x=\frac{8}{3}=2\frac{2}{3}\approx{2.667}[/tex]
