How do you solve #abs(5x + 10) - 15 = 20#?

2 Answers
Adrian D.
Aug 2, 2015

#x=-9,5#

Explanation:

Rearrange the equation:
#|5x+10|-15=20#

=>

#|5x+10|=35#

Because of the modulus there are two solutions, the first:

#5x+10=35# => #x=5#

The second:

#5x+10=-35# => #x=-9#

Meave60
Aug 2, 2015

#x=-9, 5#

Explanation:

#abs(5x+10)-15=20#

Add #15# to both sides of the equation.

#abs(5x+10)=20+15# =

#abs(5x+10)=35#

Rewrite the equation without the absolute value symbol, with one equation positive, and one negative.

#5x+10=35# and

#-(5x+10)=35#.

Positive Equation

#5x+10=35#

Subtract #10# from both sides of the equation.

#5x=35-10# =

#5x=25#

Divide both sides by #5#.

#x=25/5# =

#x=5#

Negative Equation

#-(5x+10)=35# =

#-5x-10=35#

Add #10# to both sides.

#-5x=35+10# =

#-5x=45#

Divide both sides by #-5#.

#x=45/(-5)# =

#x=-9#

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