How do you solve 6/10=(p-7)/(p+10)610=p7p+10?

1 Answer
Mar 25, 2018

The solution is p=65/2p=652.

Explanation:

First, reduce the fraction:

6/10=(p-7)/(p+10)610=p7p+10

color(Red)cancelcolor(Black)6^3/color(red)cancelcolor(black)10^5=(p-7)/(p+10)

3/5=(p-7)/(p+10)

Cross-multiply:

3(p+10)=5(p-7)

Use the distributive property:

3*p+3*10=5*p-5*7

3p+30=5p-35

3p+30color(blue)+color(blue)35=5p-35color(blue)+color(blue)35

3p+30color(blue)+color(blue)35=5pcolor(red)cancelcolor(black)(color(black)-35color(blue)+color(blue)35)

3p+30color(blue)+color(blue)35=5p

3p+65=5p

3p+65color(blue)-color(blue)(3p)=5pcolor(blue)-color(blue)(3p)

color(red)cancelcolor(black)(3p)+65color(red)cancelcolor(blue)(color(blue)-color(blue)(3p))=5pcolor(blue)-color(blue)(3p)

65=5pcolor(blue)-color(blue)(3p)

65=2p

color(blue)(color(black)65/2)=color(blue)(color(black)(2p)/2)

color(blue)(color(black)65/2)=color(blue)(color(black)(color(red)cancelcolor(black)2p)/color(red)cancelcolor(blue)2)

color(blue)(color(black)65/2)=p

This is the solution. Hope this helped!