Question

How do you solve `abs(5x)+5=45`?

Answer 1

`x++-8`

Explanation:

`"equations involving the" color(blue)" absolute value"` have 2 possible solutions.

Isolate the absolute value.

subtract 5 from both sides of the equation.

`|5x|cancel(+5)cancel(-5)=45-5`

`rArr|5x|=40`

The 2 solutions are obtained by solving `5x=color(red)(+-)40`

`color(blue)"Solution 1"`

`"solve "5x=40rArrx=8`

`color(blue)"Solution 2"`

`"solve "5x=-40rArrx=-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=8to|5xx8|+5=|40|+5=40+5 =45 color(white)(xx) ✔︎`

`x=-8to|5xx-8|+5=|-40|+5=40+5=45`

`rArrx=+-8" are the solutions"`