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

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Answer 1 · 2018-04-09T04:18:53

The solution is #p=5#.

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!