How do you solve #3abs(x+7)-14=4#?

1 Answer
Jim G.
Jun 12, 2018

#x=-13" or "x=-1#

Explanation:

#"the expression inside the absolute value can be "#
#"positive or negative hence there are 2 possible solutions"#

#"add 14 to both sides and divide by 3"#

#|x+7|=18/3=6#

#color(magenta)"positive expression"#

#x+7=6rArrx=-1#

#color(magenta)"negative expression"#

#-(x+7)=6#

#-x-7=6rArr-x=6+7=13rArrx=-13#

#color(blue)"As a check"#

Substitute these values into the equation and if the left side equals the right side then they are the solutions.

#x=-1#

#3|-1+7|-14=(3xx6)-14=18-14=4#

#x=-13#

#3||-6|-14=(3xx6)-14=18-14=4#

#x=-1" or "x=-13" are the solutions"#

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