Question 60c7e

Mar 1, 2017

$x = - 1 \text{ or } x = - 5$

Explanation:

Isolate the $\textcolor{b l u e}{\text{absolute value function}}$

divide both sides of the equation by - 3

$\frac{\cancel{- 3} | 2 x + 6 |}{\cancel{- 3}} = \frac{- 12}{- 3}$

$\Rightarrow | 2 x + 6 | = 4$

The absolute value can have a $\textcolor{b l u e}{\text{positive or negative}}$ solution.

$\Rightarrow \text{solve } 2 x + 6 = \textcolor{red}{\pm} 4$

• 2x+6=color(red)(+4)

subtract 6 from both sides.

$2 x \cancel{+ 6} \cancel{- 6} = 4 - 6$

$\Rightarrow 2 x = - 2$

divide both sides by 2

$\frac{\cancel{2} x}{\cancel{2}} = \frac{- 2}{2}$

$\Rightarrow x = - 1 \to \textcolor{red}{\left(1\right)}$

• 2x+6=-4

$\Rightarrow 2 x = - 10$

$\Rightarrow x = \frac{- 10}{2} = - 5 \to \textcolor{red}{\left(2\right)}$

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

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

• -3|-2+6|=-3|4|=-3xx4=-12

• -3|-10+6|=-3|-4|=-3xx4=-12#

$\Rightarrow x = - 1 \text{ or "x=-5" are the solutions}$