Question

How do you solve `abs(11+2x)=5`?

Answer 1

`x=-8" or "x=-3`

Explanation:

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

`color(magenta)"positive expression"`

`11+2x=5`

`"subtract 11 from both sides and divide by 2"`

`2x=5-11=-6rArrx=(-6)/2=-3`

`color(magenta)"negative expression"`

`-(11+2x)=5larr"distribute"`

`-11-2x=5`

`"add 11 to both sides and divide by "-2`

`-2x=5+11=16rArrx=16/(-2)=-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=-3to|11-6|=|5|=5`

`x=-8to|11-16|=|-5|=5`

`x=-8" or "x=-3" are the solutions"`