Precalculus Examples

3 + | 2 x | = 3 + 3

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

Step 1

Add

3

$3$ and

3

$3$ .

3 + | 2 x | = 6

$3 + | 2 x | = 6$

Step 2

Move all terms not containing

| 2 x |

$| 2 x |$ to the right side of the equation.

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Step 2.1

Subtract

3

$3$ from both sides of the equation.

| 2 x | = 6 - 3

$| 2 x | = 6 - 3$

Step 2.2

Subtract

3

$3$ from

6

$6$ .

| 2 x | = 3

$| 2 x | = 3$

| 2 x | = 3

$| 2 x | = 3$

Step 3

Remove the absolute value term. This creates a

\pm

$\pm$ on the right side of the equation because

| x | = \pm x

$| x | = \pm x$ .

2 x = \pm 3

$2 x = \pm 3$

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

$\pm$ to find the first solution.

2 x = 3

$2 x = 3$

Step 4.2

Divide each term in

2 x = 3

$2 x = 3$ by

2

$2$ and simplify.

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Step 4.2.1

Divide each term in

2 x = 3

$2 x = 3$ by

2

$2$ .

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

2

$2$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide

$x$ by

$1$ .

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

Step 4.3

Next, use the negative value of the

$\pm$ to find the second solution.

$2 x = - 3$

Step 4.4

Divide each term in

$2 x = - 3$ by

$2$ and simplify.

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Step 4.4.1

Divide each term in

$2 x = - 3$ by

$2$ .

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of

$2$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

Step 4.4.2.1.2

Divide

$x$ by

$1$ .

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

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

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

Step 4.5

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5, - 1.5$

Mixed Number Form:

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

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