Precalculus Examples

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

Add $2$ and $3$ .

$| 2 y | + 3 = 5$

Move all terms not containing $| 2 y |$ to the right side of the equation.

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Subtract $3$ from both sides of the equation.

$| 2 y | = - 3 + 5$

Add $- 3$ and $5$ .

$| 2 y | = 2$

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

$2 y = \pm 2$

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

$2 y = 2$

Divide each term by $2$ and simplify.

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

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Divide $2$ by $2$ .

$y = 1$

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

$2 y = - 2$

Solve the second equation for $y$ .

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Multiply $- 1$ by $2$ .

$2 y = - 2$

Divide each term by $2$ and simplify.

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

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side of the equation.

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Divide $2$ by $2$ .

$y = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$y = - 1$

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

$y = 1, - 1$

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