Precalculus Examples

$| 3 y | + 3 = 3$

Move all terms not containing $| 3 y |$ to the right side of the equation.

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Subtract $3$ from both sides of the equation.

$| 3 y | = 3 - 3$

Subtract $3$ from $3$ .

$| 3 y | = 0$

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

$3 y = \pm 0$

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

$3 y = 0$

Divide each term by $3$ and simplify.

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Divide each term in $3 y = 0$ by $3$ .

$\frac{3 y}{3} = \frac{0}{3}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{3 y}{3} = \frac{0}{3}$

Divide $y$ by $1$ .

$y = \frac{0}{3}$

Divide $0$ by $3$ .

$y = 0$

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

$3 y = 0$

Divide each term by $3$ and simplify.

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Divide each term in $3 y = 0$ by $3$ .

$\frac{3 y}{3} = \frac{0}{3}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{3 y}{3} = \frac{0}{3}$

Divide $y$ by $1$ .

$y = \frac{0}{3}$

Divide $0$ by $3$ .

$y = 0$

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

$y = 0$

Verify each of the solutions by substituting them into $| 3 y | + 3 = 3$ and solving.

$y = 0$

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