Algebra Examples

2 + 2 = | 2 x |

$2 + 2 = | 2 x |$

Step 1

Rewrite the equation as

| 2 x | = 2 + 2

$| 2 x | = 2 + 2$ .

| 2 x | = 2 + 2

$| 2 x | = 2 + 2$

Step 2

Add

2

$2$ and

2

$2$ .

| 2 x | = 4

$| 2 x | = 4$

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 4

$2 x = \pm 4$

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 = 4

$2 x = 4$

Step 4.2

Divide each term in

2 x = 4

$2 x = 4$ by

2

$2$ and simplify.

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Step 4.2.1

Divide each term in

2 x = 4

$2 x = 4$ by

2

$2$ .

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

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

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.

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

Step 4.2.2.1.2

Divide

$x$ by

$1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide

$4$ by

$2$ .

$x = 2$

Step 4.3

Next, use the negative value of the

$\pm$ to find the second solution.

$2 x = - 4$

Step 4.4

Divide each term in

$2 x = - 4$ by

$2$ and simplify.

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Step 4.4.1

Divide each term in

$2 x = - 4$ by

$2$ .

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

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.

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

Step 4.4.2.1.2

Divide

$x$ by

$1$ .

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

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide

$- 4$ by

$2$ .

$x = - 2$

Step 4.5

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

$x = 2, - 2$

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