Question

How do you solve `abs(15-3x)=12`?

Answer 1

`x=1" or " x=9`

Explanation:

There are 2 solutions to the equation.

`"solving "15-3x=color(red)(+-)12`

`color(blue)"first solution"`

`"solve "15-3x=color(red)(+12)`

subtract 15 from both sides of the equation.

`cancel(15)cancel(-15)-3x=12-15`

`rArr-3x=-3`

divide both sides by - 3

`(cancel(-3) x)/cancel(-3)=(-3)/(-3)`

`rArrx=1`

`color(blue)"second solution"`

`"solve "15-3x=color(red)(-12)`

`rArr-3x=-12-15=-27`

`rArrx=(-27)/(-3)=9`

`color(magenta)"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=1to|15-(3xx1)|=|12|=12larr" true"`

`• x=9 to|15-(3xx9)|=|-12|=12larr" true"`

`rArr" solutions are "x=1" or "x=9`