Question

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

Answer 1

The solutions are `x=0,10`.

Explanation:

There are two possible solutions to an absolute value equation.

For example, the solutions for `|x|=1` are `x=1` and `x=-1`, because the absolute values of `1` and `-1` are both `1`.

The equation `|x-5|=5` splits into to solutions: `x-5=5` and `x-5=-5`. Now, solve for `x` in both of the new equations.

`qquadqquadqquadqquad|x-5|=5`
`" ↙ ↘"`
`color(white){color(black)( (x-5=5, qquadqquad x-5=-5), (x=10, qquadqquad x=0)):}`

Those are the two solutions. We can verify them by plugging them into the original equation:

`|x-5|=5`

Check `0`:

`|0-5|=5`

`|-5|=5`

`5=5" "sqrt`

The solution `0` works. Check `10`:

`|10-5|=5`

`|5|=5`

`5=5" "sqrt`

The solution `10` also works, so both solutions are correct. Hope this helps.

Answer 2

`x=0 or 10`

Explanation:

`x-5 =5` or `x-5=-5`
`x=5+5` or `x=-5+5`
`x=10` or `x=0`