How do you solve #2( p + 1) = 3( p - 1)#?

1 Answer
Apr 9, 2018

The solution is #p=5#.

Explanation:

Use the distributive property to expand the multiplication:

#color(blue)2(p+1)=color(red)3(p-1)#

#color(blue)2*p+color(blue)2*1=color(red)3*p-color(red)3*1#

#2p+2=3p-3#

#2p+2color(blue)+color(blue)3=3p-3color(blue)+color(blue)3#

#2p+2color(blue)+color(blue)3=3pcolor(red)cancelcolor(black)(color(black)-3color(blue)+color(blue)3)#

#2p+2color(blue)+color(blue)3=3p#

#2p+5=3p#

#2p+5color(blue)-color(blue)(2p)=3pcolor(blue)-color(blue)(2p)#

#color(red)cancelcolor(black)(2p)+5color(red)cancelcolor(blue)(color(blue)-color(blue)(2p))=3pcolor(blue)-color(blue)(2p)#

#5=3pcolor(blue)-color(blue)(2p)#

#5=p#

#p=5#

That's the solution. Hope this helped!