Algebra Examples

$4 | 2 x + 3 | + 8 = 20$

Step 1

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

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Step 1.1

Subtract $8$ from both sides of the equation.

$4 | 2 x + 3 | = 20 - 8$

Step 1.2

Subtract $8$ from $20$ .

$4 | 2 x + 3 | = 12$

Step 2

Divide each term in $4 | 2 x + 3 | = 12$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 | 2 x + 3 | = 12$ by $4$ .

$\frac{4 | 2 x + 3 |}{4} = \frac{12}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 | 2 x + 3 |}{4} = \frac{12}{4}$

Step 2.2.1.2

Divide $| 2 x + 3 |$ by $1$ .

$| 2 x + 3 | = \frac{12}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $12$ by $4$ .

$| 2 x + 3 | = 3$

Step 3

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

$2 x + 3 = \pm 3$

Step 4

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

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Step 4.1

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

$2 x + 3 = 3$

Step 4.2

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

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$2 x = 3 - 3$

Step 4.2.2

Subtract $3$ from $3$ .

$2 x = 0$

Step 4.3

Divide each term in $2 x = 0$ by $2$ and simplify.

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Step 4.3.1

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $0$ by $2$ .

$x = 0$

Step 4.4

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

$2 x + 3 = - 3$

Step 4.5

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

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Step 4.5.1

Subtract $3$ from both sides of the equation.

$2 x = - 3 - 3$

Step 4.5.2

Subtract $3$ from $- 3$ .

$2 x = - 6$

Step 4.6

Divide each term in $2 x = - 6$ by $2$ and simplify.

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Step 4.6.1

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Cancel the common factor of $2$ .

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Step 4.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Divide $- 6$ by $2$ .

$x = - 3$

Step 4.7

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

$x = 0, - 3$