Examples

| 2 y | + 3 = 2 + 3

$| 2 y | + 3 = 2 + 3$

Step 1

Add

2

$2$ and

3

$3$ .

| 2 y | + 3 = 5

$| 2 y | + 3 = 5$

Step 2

Move all terms not containing

| 2 y |

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

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Step 2.1

Subtract

3

$3$ from both sides of the equation.

| 2 y | = 5 - 3

$| 2 y | = 5 - 3$

Step 2.2

Subtract

3

$3$ from

5

$5$ .

| 2 y | = 2

$| 2 y | = 2$

| 2 y | = 2

$| 2 y | = 2$

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 y = \pm 2

$2 y = \pm 2$

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 y = 2

$2 y = 2$

Step 4.2

Divide each term in

2 y = 2

$2 y = 2$ by

2

$2$ and simplify.

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Step 4.2.1

Divide each term in

2 y = 2

$2 y = 2$ by

2

$2$ .

\frac{2 y}{2} = \frac{2}{2}

$\frac{2 y}{2} = \frac{2}{2}$

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.

$\frac{2 y}{2} = \frac{2}{2}$

Step 4.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{2}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide

$2$ by

$2$ .

$y = 1$

Step 4.3

Next, use the negative value of the

$\pm$ to find the second solution.

$2 y = - 2$

Step 4.4

Divide each term in

$2 y = - 2$ by

$2$ and simplify.

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Step 4.4.1

Divide each term in

$2 y = - 2$ by

$2$ .

$\frac{2 y}{2} = \frac{- 2}{2}$

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.

$\frac{2 y}{2} = \frac{- 2}{2}$

Step 4.4.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{- 2}{2}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide

$- 2$ by

$2$ .

$y = - 1$

Step 4.5

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

$y = 1, - 1$

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