How do you solve abs(15-3x)=12?

1 Answer
Feb 21, 2017

$x = 1 \text{ or } x = 9$

Explanation:

There are 2 solutions to the equation.

$\text{solving } 15 - 3 x = \textcolor{red}{\pm} 12$

$\textcolor{b l u e}{\text{first solution}}$

$\text{solve } 15 - 3 x = \textcolor{red}{+ 12}$

subtract 15 from both sides of the equation.

$\cancel{15} \cancel{- 15} - 3 x = 12 - 15$

$\Rightarrow - 3 x = - 3$

divide both sides by - 3

$\frac{\cancel{- 3} x}{\cancel{- 3}} = \frac{- 3}{- 3}$

$\Rightarrow x = 1$

$\textcolor{b l u e}{\text{second solution}}$

$\text{solve } 15 - 3 x = \textcolor{red}{- 12}$

$\Rightarrow - 3 x = - 12 - 15 = - 27$

$\Rightarrow x = \frac{- 27}{- 3} = 9$

$\textcolor{m a \ge n t a}{\text{As a check}}$

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

• x=1to|15-(3xx1)|=|12|=12larr" true"

• x=9 to|15-(3xx9)|=|-12|=12larr" true"

$\Rightarrow \text{ solutions are "x=1" or } x = 9$