Calculus Examples

2 + | 3 x | = 2 + 3

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

Step 1

Add

2

$2$ and

3

$3$ .

2 + | 3 x | = 5

$2 + | 3 x | = 5$

Step 2

Move all terms not containing

| 3 x |

$| 3 x |$ to the right side of the equation.

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Step 2.1

Subtract

2

$2$ from both sides of the equation.

| 3 x | = 5 - 2

$| 3 x | = 5 - 2$

Step 2.2

Subtract

2

$2$ from

5

$5$ .

| 3 x | = 3

$| 3 x | = 3$

| 3 x | = 3

$| 3 x | = 3$

Step 3

Remove the absolute value term. This creates a

\pm

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

| x | = \pm x

$| x | = \pm x$ .

3 x = \pm 3

$3 x = \pm 3$

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.

3 x = 3

$3 x = 3$

Step 4.2

Divide each term in

3 x = 3

$3 x = 3$ by

3

$3$ and simplify.

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Step 4.2.1

Divide each term in

3 x = 3

$3 x = 3$ by

3

$3$ .

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of

3

$3$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

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

Step 4.2.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{3}{3}

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

x = \frac{3}{3}

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

x = \frac{3}{3}

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide

3

$3$ by

3

$3$ .

x = 1

$x = 1$

x = 1

$x = 1$

x = 1

$x = 1$

Step 4.3

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

3 x = - 3

$3 x = - 3$

Step 4.4

Divide each term in

3 x = - 3

$3 x = - 3$ by

3

$3$ and simplify.

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Step 4.4.1

Divide each term in

3 x = - 3

$3 x = - 3$ by

3

$3$ .

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

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of

3

$3$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

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

Step 4.4.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 3}{3}

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

x = \frac{- 3}{3}

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

x = \frac{- 3}{3}

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

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide

- 3

$- 3$ by

3

$3$ .

x = - 1

$x = - 1$

x = - 1

$x = - 1$

x = - 1

$x = - 1$

Step 4.5

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

x = 1, - 1

$x = 1, - 1$

x = 1, - 1

$x = 1, - 1$

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