Precalculus Examples

$| 3 x - 2 | + 3 = 3$

Step 1

Move all terms not containing $| 3 x - 2 |$ to the right side of the equation.

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Step 1.1

Subtract $3$ from both sides of the equation.

$| 3 x - 2 | = 3 - 3$

Step 1.2

Subtract $3$ from $3$ .

$| 3 x - 2 | = 0$

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$3 x - 2 = \pm 0$

Step 3

Plus or minus $0$ is $0$ .

$3 x - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$3 x = 2$

Step 5

Divide each term in $3 x = 2$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$