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

Apr 24, 2017

$x = 27 , - 7$

#### Explanation:

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

$| x - 10 | = 17$

$| - 7 - 10 | = 17$

$| - 17 | = 17$

$17 = 17$

Apr 24, 2017

$x = - 7 \text{ or } x = 27$

#### Explanation:

The value inside the $\textcolor{b l u e}{\text{absolute value function}}$ can be positive or negative. This means there are 2 possible solutions.

$| x = 10 | = 17$

$\Rightarrow x - 10 = \textcolor{red}{\pm} 17$

$\left(1\right) \text{ solve } x - 10 = \textcolor{red}{+} 17$

$\text{add 10 to both sides}$

$x \cancel{- 10} \cancel{+ 10} = 17 + 10$

$\Rightarrow x = 27 \text{ is a possible solution}$

$\left(2\right) \text{ solve } x - 10 = \textcolor{red}{-} 17$

$\text{add 10 to both sides}$

$\Rightarrow x = - 17 + 10$

$\Rightarrow x = - 7 \text{ is a possible solution}$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

$\text{left side "=|27-10|=|17|=17=" right side}$

$\text{left side "=|-7-10|=|-17|=17=" right side}$

$\Rightarrow x = - 7 \text{ or " x=27" are the solutions}$