Pre-Algebra Examples

$| 3 x - 2 | + 4 = 11$

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 $4$ from both sides of the equation.

$| 3 x - 2 | = 11 - 4$

Step 1.2

Subtract $4$ from $11$ .

$| 3 x - 2 | = 7$

Step 2

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

$3 x - 2 = \pm 7$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$3 x - 2 = 7$

Step 3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.2.1

Add $2$ to both sides of the equation.

$3 x = 7 + 2$

Step 3.2.2

Add $7$ and $2$ .

$3 x = 9$

Step 3.3

Divide each term in $3 x = 9$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $9$ by $3$ .

$x = 3$

Step 3.4

Next, use the negative value of the $\pm$ to find the second solution.

$3 x - 2 = - 7$

Step 3.5

Move all terms not containing $x$ to the right side of the equation.

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Step 3.5.1

Add $2$ to both sides of the equation.

$3 x = - 7 + 2$

Step 3.5.2

Add $- 7$ and $2$ .

$3 x = - 5$

Step 3.6

Divide each term in $3 x = - 5$ by $3$ and simplify.

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Step 3.6.1

Divide each term in $3 x = - 5$ by $3$ .

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

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $3$ .

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Step 3.6.2.1.1

Cancel the common factor.

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

Step 3.6.2.1.2

Divide $x$ by $1$ .

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

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Move the negative in front of the fraction.

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

Step 3.7

The complete solution is the result of both the positive and negative portions of the solution.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 3, - 1.\overline{6}$

Mixed Number Form:

$x = 3, - 1 \frac{2}{3}$