Algebra Examples

$| 2 y | = 3 + 2$

Step 1

Add $3$ and $2$ .

$| 2 y | = 5$

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$2 y = \pm 5$

Step 3

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

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First, use the positive value of the $\pm$ to find the first solution.

$2 y = 5$

Divide each term in $2 y = 5$ by $2$ and simplify.

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Divide each term in $2 y = 5$ by $2$ .

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

Simplify the left side.

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Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Next, use the negative value of the $\pm$ to find the second solution.

$2 y = - 5$

Divide each term in $2 y = - 5$ by $2$ and simplify.

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Divide each term in $2 y = - 5$ by $2$ .

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

Simplify the left side.

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Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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Move the negative in front of the fraction.

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 2.5, - 2.5$

Mixed Number Form:

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

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