How do you solve #\frac { x + 2} { 9} - \frac { 2x + 9} { 5} = 2x + 3#?

1 Answer
Sep 13, 2017

#x=-2#

Explanation:

#(x+2)/9-(2x+9)/5=2x+3#

Multiplying first term by #5/5# and the second by #9/9# on the right side of the equation to get a common denominator:
#((x+2)*5)/(9*5)-((2x+9)*9)/(5*9)=2x+3#
#(5x+10)/45-(18x+81)/45=2x+3#
#((5x+10)-(18x+81))/45=2x+3#

Simple simplification:
#(5x+10-18x-81)/45=2x+3#

Then we multiply both sides of the equation by 45 to get rid of denominator on the left side of the equation:
#(5x+10-18x-81)/cancel(45)*cancel(45)=(2x+3)*45#
#5x+10-18x-81=90x+135#

Grouping like-terms next to each other and then evaluating them:
#5x-18x+10-81=90x+135#
#-13x-71=90x+135#

Adding 13x to both sides of the equation to get the terms with x in it to one side:
#cancel(13x)-71+cancel(13x)=90x+135+13x#
#-71=103x+135#

Then we subtract 135 from both sides to isolate the term that has the unknown x in it:
#-71-135=103xcancel(+135)-cancel(135)#
#-206=103x#

Then we divide both sides of equation by 103 to isolate x:
#(cancel(-206)-2)/cancel(103)=(cancel(103)x)/cancel103#
#-2=x#

#rarr color(red)(x=-2)#