How do you solve #-(5x+9)/2 +3/2=-(7x)/3#?

1 Answer
Jul 30, 2017

#x=-18#

Refer to the explanation for the process.

Explanation:

Solve:

#-(5x+9)/2 + 3/2=-(7x)/3#

Since the fractions on the left side have the same denominator, place both numerators can be placed over the denominator.

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

Simplify the parentheses.

#(-5x-9+3)/2=-(7x)/3#

Simplify.

#(-5x-6)/2=-(7x)/3#

Multiply both sides by the least common denominator (LCD) of #6#.

#(6(-5x-6))/2=(6(-7x))/3#

Simplify.

#(color(red)cancel(color(black)(6^color(blue)3))(-5x-6))/color(red)cancel(color(black)(2^color(blue)1))=(color(red)cancel(color(black)(6^color(blue)2))(-7x))/color(red)cancel(color(black)(3^color(blue)1))#

#3(-5x-6)=2(-7x)#

Expand.

#-15x-18=-14x#

Add #15x# to both sides.

#-15x+15x-18=-14x+15x#

Cancel #15x# on the left side.

Simplify.

#-color(red)cancel(color(black)(15x))+color(red)cancel(color(black)(15x))-18=-14x+15x#

Simplify.

#-18=x#

Switch sides.

#x=-18#