# How do you solve abs(t+6)=4?

Sep 18, 2016

$t = - 10 \text{ and } t = - 2$

#### Explanation:

The value inside the $\textcolor{b l u e}{\text{absolute value}}$ can be positive or negative but always produces a positive answer.

For example : $| - 4 | = 4 \text{ and} | 4 | = 4$

The absolute value informs us about how far the number is from the origin with no consideration of it's direction.

$- 4 \mathmr{and} + 4 \text{ are both 4 units from the origin.}$

This is also true for algebraic expressions inside the absolute value bars, so

$t + 6 = 4 \Rightarrow t = 4 - 6 \Rightarrow t = - 2$

and

$- \left(t + 6\right) = 4 \Rightarrow - t - 6 = 4$

$- t \cancel{- 6} \cancel{+ 6} = 4 + 6$
$\Rightarrow - t = 10 \Rightarrow t = - 10$
Check : $t = - 2 \Rightarrow | - 2 + 6 | = | 4 | = 4$
and $t = - 10 \Rightarrow | - 10 + 6 | = | - 4 | = 4$