Question

How do you solve `abs(15-2x)=8`?

Answer 1

`x=7/2" or " x=23/2`

Explanation:

There are 2 possible solutions to this type of equation.

Removing the 'bars' gives.

`15-2x=color(red)(+-)8`

`• " solve " 15-2x=color(red)(+)8`

subtract 15 to both sides.

`cancel(15)cancel(-15)-2x=8-15`

`rArr-2x=-7`

divide both side by - 2

`(cancel(-2) x)/cancel(-2)=(-7)/(-2)`

`rArrx=7/2`

`• " solve " 15-2x=color(red)(-)8`

`rArr-2x=-23`

`rArrx=23/2`

`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.

`|15-2xx7/2|=|8|=8`

`|15-2xx23/2|=|-8|=8`

`rArrx=7/2" or " x=23/2" are the solutions"`