How do you solve `abs(x-10)=17`?

With absolute value equations, you need to evaluate both negative and positive circumstances of the absolute value.

`|x-10|=17`

AND

`|x-10|=-17`

[We ignore the absolute value sign until we check our answers]

So,

`x-10=17`

`x=17+10`

`x=27`

AND

`x-10=-17`

`x=-17+10`

`x=-7`

Therefore, our two values for `x` are `27` and `-7`

I'll check them below for reference.
[Remember to substitute your values only into the original equation!]

`|x-10|=17`

`|27-10|=17`

`|17|=17`

`17=17`

OR

`|x-10|=17`

`|-7-10|=17`

`|-17|=17`

`17=17`

The value inside the `color(blue)"absolute value function"` can be positive or negative. This means there are 2 possible solutions.

`|x=10|=17`

`rArrx-10=color(red)(+-)17`

`(1)" solve " x-10=color(red)(+)17`

`"add 10 to both sides"`

`xcancel(-10)cancel(+10)=17+10`

`rArrx=27" is a possible solution"`

`(2)" solve " x-10=color(red)(-)17`

`"add 10 to both sides"`

`rArrx=-17+10`

`rArrx=-7" is a possible solution"`

`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.

`"left side "=|27-10|=|17|=17=" right side"`

`"left side "=|-7-10|=|-17|=17=" right side"`

`rArrx=-7" or " x=27" are the solutions"`