How do you solve $abs(3x+2)=2$ ?

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Answer 1 · 2015-07-16T23:58:28

$color(red)(x = 0)$ and $color(red)(x = -4/3)$ .

We need to write two different equations without the absolute value symbols and solve for $x$ .

These equations would be

(1): $(3x+2) = 2$
(2): $-(3x+2) = 2$

Solve Equation 1:

$3x+2 = 2$

Subtract $2$ from each side.

$3x = 0$

Divide each side by $3$ .

$x = 0$

Solve Equation 2.

$−(3x+2) = 2$

Remove parentheses.

$−3x−2= 2$

Add $2$ to each side.

$-3x = 4$

Divide each side by $-3$ .

$x = -4/3$

The solutions are $x = 0$ and $x = -4/3$ .

Check:

If $x = 0$ ,

$|3x+2|=2$
$|3×0 +2|= 2$
$|0 + 2| = 2$
$|2| =2$
$2=2$

If $x= -4/3$ ,

$|3x+2|=2$
$|3×(-4/3) + 2| = 2$
$|-4 + 2| = 2$
$|-2| = 2$
$2 = 2$

How do you solve abs(3x+2)=2abs(3x+2)=2?