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

##### 2 Answers

#### Explanation:

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

AND

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

So,

AND

Therefore, our two values for

I'll check them below for reference.

**[Remember to substitute your values only into the original equation!]**

OR

#### Explanation:

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"#