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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