# How do you solve  2| 3x - 2 | = 14?

Mar 20, 2016

$x = 3 , - \frac{5}{3}$

#### Explanation:

Understand that:

$\therefore$ Absolute values are always mean the distance from $0$

eg,$| - 7 | = 7 , | 4 | = 4$

color(blue)(2|3x-2|=14

Divide both sides by $2$

$\rightarrow \frac{\cancel{2} | 3 x - 2 |}{\cancel{2}} = \frac{14}{2}$

$\rightarrow | 3 x - 2 | = 7$

Now we can write that

color(brown)(3x-2=7,3x-2=-7

Solve for both the equations

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$

color(orange)(3x-2=7

$\rightarrow 3 x = 7 + 2$

$\rightarrow 3 x = 9$

color(green)(rArrx=9/3=3

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$

color(indigo)(3x-2=-7

$\rightarrow 3 x = - 7 + 2$

$\rightarrow 3 x = - 5$

color(green)(rArrx=-5/3

Mar 20, 2016

$| 3 x - 2 | = 7$ is the combined equation for the couple
$3 x - 2 = 7 \mathmr{and} 2 - 3 x = 7$