Algebra Examples

| 2 y | = 3 + 2

$| 2 y | = 3 + 2$

Step 1

Add

3

$3$ and

2

$2$ .

| 2 y | = 5

$| 2 y | = 5$

Step 2

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 5

$2 y = \pm 5$

Step 3

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

Tap for more steps...

Step 3.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

2 y = 5

$2 y = 5$

Step 3.2

Divide each term in

2 y = 5

$2 y = 5$ by

2

$2$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in

2 y = 5

$2 y = 5$ by

2

$2$ .

\frac{2 y}{2} = \frac{5}{2}

$\frac{2 y}{2} = \frac{5}{2}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

\frac{2 y}{2} = \frac{5}{2}

$\frac{2 y}{2} = \frac{5}{2}$

Step 3.2.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{5}{2}

$y = \frac{5}{2}$

y = \frac{5}{2}

$y = \frac{5}{2}$

y = \frac{5}{2}

$y = \frac{5}{2}$

y = \frac{5}{2}

$y = \frac{5}{2}$

Step 3.3

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

2 y = - 5

$2 y = - 5$

Step 3.4

Divide each term in

2 y = - 5

$2 y = - 5$ by

2

$2$ and simplify.

Tap for more steps...

Step 3.4.1

Divide each term in

2 y = - 5

$2 y = - 5$ by

2

$2$ .

\frac{2 y}{2} = \frac{- 5}{2}

$\frac{2 y}{2} = \frac{- 5}{2}$

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor.

\frac{2 y}{2} = \frac{- 5}{2}

$\frac{2 y}{2} = \frac{- 5}{2}$

Step 3.4.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{- 5}{2}

$y = \frac{- 5}{2}$

y = \frac{- 5}{2}

$y = \frac{- 5}{2}$

y = \frac{- 5}{2}

$y = \frac{- 5}{2}$

Step 3.4.3

Simplify the right side.

Tap for more steps...

Step 3.4.3.1

Move the negative in front of the fraction.

y = - \frac{5}{2}

$y = - \frac{5}{2}$

y = - \frac{5}{2}

$y = - \frac{5}{2}$

y = - \frac{5}{2}

$y = - \frac{5}{2}$

Step 3.5

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

y = \frac{5}{2}, - \frac{5}{2}

$y = \frac{5}{2}, - \frac{5}{2}$

y = \frac{5}{2}, - \frac{5}{2}

$y = \frac{5}{2}, - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

y = \frac{5}{2}, - \frac{5}{2}

$y = \frac{5}{2}, - \frac{5}{2}$

Decimal Form:

y = 2.5, - 2.5

$y = 2.5, - 2.5$

Mixed Number Form:

y = 2 \frac{1}{2}, - 2 \frac{1}{2}

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

Enter YOUR Problem