# How do you solve -3| a - 1| = - 15?

Feb 25, 2018

-4 and 6.

#### Explanation:

Start by isolating the absolute value (it contains the variable you're solving for, a.)

Dividing both sides by -3 we get |a-1| = 5

Then, split this into two parts:

$a - 1 = 5$
and
$a - 1 = - 5$

Solve for a in both of those, and you should have your answers.

The reason we split it into two equations to remove the absolute value symbols is because those symbols make a negative number positive. If the variable inside is negative, it will be made positive. This must be reflected when we're solving an equation like this.

For example, $| - 30 | = 30$.
But $| 30 | = 30$ too.
Now imagine if a variable a was in those bars.
|a| = ?  The answer could be positive OR negative!

Hope this makes sense.

Feb 25, 2018

$a = - 4 \text{ " " " \text{or} " " " } a = 6$

are the required solutions.




#### Explanation:

$- 3 | a - 1 | = - 15$

Divide both sides by $- 3$ to isolate the absolute value on the left hand side:

$\setminus \frac{- 3 | a - 1 |}{- 3} = \setminus \frac{- 15}{- 3}$

Simplify:

$| a - 1 | = 5$



For an absolute value equation, there are two solutions.

$| f \left(a\right) | = a \text{ " rightarrow " " f(a)=-a " " " " \text{or} " " " } f \left(a\right) = a$



$a - 1 = - 5 \text{ " " " \text{or} " " " } a - 1 = 5$

$a = - 4 \text{ " " " \text{or} " " " } a = 6$



That's it!