Algebra Examples

$| 2 y | = 3 + 2$

Add $3$ and $2$ .

$| 2 y | = 5$

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

$2 y = \pm 5$

Set up the positive portion of the $\pm$ solution.

$2 y = 5$

Divide each term by $2$ and simplify.

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

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Set up the negative portion of the $\pm$ solution.

$2 y = - 5$

Solve the second equation for $y$ .

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Multiply $- 1$ by $5$ .

$2 y = - 5$

Divide each term by $2$ and simplify.

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

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

The solution to the equation includes both the positive and negative portions of the solution.

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

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