How do you solve $2 | 3 x - 2 | = 14$ $2abs(3x - 2 ) = 14$ ?

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Answer 1 · 2015-06-28T19:58:50

There are two possible answers:

$x_{1} = 3$ $x_1=3$

$x_{2} = - \frac{5}{3}$ $x_2=-5/3$

$2 | 3 x - 2 | = 14 \to | 3 x - 2 | = 7$ $2abs(3x-2)=14 rarr abs(3x-2)=7$

Knowing that $| x | = | - x |$ $abs(x)=abs(-x)$ we now have two possibilities:

$3 x - 2 = 7$ $3x-2=7$ or
$3 x - 2 = - 7$ $3x-2=-7$

I) $3 x - 2 = 7 \to 3 x = 7 + 2 = 9 \to x = \frac{9}{3} = 3$ $3x-2=7 rarr 3x=7+2=9 rarr x=9/3=3$

II) $3 x - 2 = - 7 \to 3 x = - 7 + 2 = - 5 \to x = - \frac{5}{3}$ $3x-2=-7 rarr 3x=-7+2=-5 rarr x=-5/3$

How do you solve 2|3x−2|=142abs(3x - 2 ) = 14?