Question

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

Answer 1

`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"`