Precalculus Examples

$| 2 x + 1 | - 3$

Step 1

Set $| 2 x + 1 | - 3$ equal to $0$ .

$| 2 x + 1 | - 3 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $3$ to both sides of the equation.

$| 2 x + 1 | = 3$

Step 2.2

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

$2 x + 1 = \pm 3$

Step 2.3

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

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Step 2.3.1

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

$2 x + 1 = 3$

Step 2.3.2

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

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Step 2.3.2.1

Subtract $1$ from both sides of the equation.

$2 x = 3 - 1$

Step 2.3.2.2

Subtract $1$ from $3$ .

$2 x = 2$

Step 2.3.3

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

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Step 2.3.3.1

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

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

Step 2.3.3.2

Simplify the left side.

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Step 2.3.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.3.2.1.1

Cancel the common factor.

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

Step 2.3.3.2.1.2

Divide $x$ by $1$ .

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

Step 2.3.3.3

Simplify the right side.

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Step 2.3.3.3.1

Divide $2$ by $2$ .

$x = 1$

Step 2.3.4

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

$2 x + 1 = - 3$

Step 2.3.5

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

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Step 2.3.5.1

Subtract $1$ from both sides of the equation.

$2 x = - 3 - 1$

Step 2.3.5.2

Subtract $1$ from $- 3$ .

$2 x = - 4$

Step 2.3.6

Divide each term in $2 x = - 4$ by $2$ and simplify.

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Step 2.3.6.1

Divide each term in $2 x = - 4$ by $2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Step 2.3.6.2

Simplify the left side.

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Step 2.3.6.2.1

Cancel the common factor of $2$ .

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Step 2.3.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Step 2.3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{2}$

Step 2.3.6.3

Simplify the right side.

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Step 2.3.6.3.1

Divide $- 4$ by $2$ .

$x = - 2$

Step 2.3.7

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

$x = 1, - 2$

Step 3