How do you solve #| 2x - 5 | + 3 = 12#?

2 Answers
Mar 3, 2018

Answer:

#x = 7, -2#

Explanation:

#|2x - 5| + 3 = 12# Given Equation

#|2x - 5| = 9# Subtracted #3# from both sides

#|2x| = 14# Added #5# to each side.

#x = 7# Divided 2 by both sides

Since this is absolute value, you are also required to also solve the equation where in this case #x# could also be negative aswell as positive.

#-|2x - 5| + 3 = 12#

#-2x + 5 + 3 = 12# Distributed the negative sign.

#-2x + 8 = 12# Added 5 and 3.

#-2x = 4# Subtracted 8 from 12.

#x = -2# Divided -2 to 4.

Mar 3, 2018

Answer:

#x=-2,7#

Explanation:

Solve:

#abs(2x-5)+3=12#

Since #abs(a)=a and -a#, the equation can be broken into two equations:

#2x-5+3=12# and #-(2x-5)+3=12#

Solve the first equation:

#2x-5+3=12#

Simplify #(-5+3)# to #-2#.

#2x-2=12#

Add #2# to both sides of the equation.

#2x=12+2#

Simplify.

#2x=14#

Divide both sides by #2#.

#x=14/2#

#x=7#

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Solve the second equation:

#-(2x-5)+3=12#

Expand.

#-2x+5+3=12#

Simplify #(5+3)# to #8#.

#-2x+8=12#

Subtract #8# from #12#

#-2x=12-8#

Simplify.

#-2x=4#

Divide both sides by #-2#.

#x=4/(-2)#

#x=-2#

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#x=-2,7#