Question

How do you solve `8abs(x+7)-3=5`?

Answer 1

`x=-8" or "x=-6`

Explanation:

`"the expression inside the absolute value bars can be"`
`"positive or negative hence we have to consider both"`

`"isolate "|x+7|" by adding 3 to both sides"`

`8|x+7|cancel(-3)cancel(+3)=5+3`

`rArr8|x+7|=8`

`"divide both sides by 8"`

`cancel(8)/cancel(8)|x+7|=8/8`

`rArr|x+7|=1`

`"consider the "color(magenta)" positive value ""of "x+7`

`rArrx+7=1larr"subtract 7 from both sides"`

`rArrx=1-7=-6`

`"consider the "color(magenta)"negative value ""of "x+7`

`rArr-(x+7)=1larr"distribute"`

`rArr-x-7=1larr"add 7 to both sides"`

`rArr-x=1+7=8`

`rArrx=-8`

`color(blue)"As a check"`

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

`x=-6to8|-6+7|-3=8-3=5`

`x=-8to8|-8+7|-3=8|-1|-3=8-3=5`

`rArrx=-8" or "x=-6" are the solutions"`