Precalculus Examples

$| 4 x - 12 |$

The piecewise polynomials are $4 x - 12$ when $4 x - 12 \geq 0$ and $(- 1) (4 x - 12)$ when $4 x - 12 < 0$ .

${\begin{cases} (4 x - 12) & 4 x - 12 \geq 0 \\ (- 1) (4 x - 12) & 4 x - 12 < 0 \end{cases}$

Remove parentheses.

${\begin{cases} 4 x - 12 & 4 x - 12 \geq 0 \\ (- 1) (4 x - 12) & 4 x - 12 < 0 \end{cases}$

Solve for $x$ when $4 x - 12 \geq 0$ .

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Add $12$ to both sides of the inequality.

${\begin{cases} 4 x - 12 & 4 x \geq 12 \\ (- 1) (4 x - 12) & 4 x - 12 < 0 \end{cases}$

Divide each term by $4$ and simplify.

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Divide each term in $4 x \geq 12$ by $4$ .

${\begin{cases} 4 x - 12 & \frac{4 x}{4} \geq \frac{12}{4} \\ (- 1) (4 x - 12) & 4 x - 12 < 0 \end{cases}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

${\begin{cases} 4 x - 12 & \frac{4 x}{4} \geq \frac{12}{4} \\ (- 1) (4 x - 12) & 4 x - 12 < 0 \end{cases}$

Divide $x$ by $1$ .

${\begin{cases} 4 x - 12 & x \geq \frac{12}{4} \\ (- 1) (4 x - 12) & 4 x - 12 < 0 \end{cases}$

Divide $12$ by $4$ .

${\begin{cases} 4 x - 12 & x \geq 3 \\ (- 1) (4 x - 12) & 4 x - 12 < 0 \end{cases}$

Simplify $(- 1) (4 x - 12)$ .

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Apply the distributive property.

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 1 (4 x) - 1 \cdot - 12 & 4 x - 12 < 0 \end{cases}$

Multiply.

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Multiply $4$ by $- 1$ .

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 4 x - 1 \cdot - 12 & 4 x - 12 < 0 \end{cases}$

Multiply $- 1$ by $- 12$ .

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 4 x + 12 & 4 x - 12 < 0 \end{cases}$

Solve for $x$ when $4 x - 12 < 0$ .

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Add $12$ to both sides of the inequality.

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 4 x + 12 & 4 x < 12 \end{cases}$

Divide each term by $4$ and simplify.

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Divide each term in $4 x < 12$ by $4$ .

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 4 x + 12 & \frac{4 x}{4} < \frac{12}{4} \end{cases}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 4 x + 12 & \frac{4 x}{4} < \frac{12}{4} \end{cases}$

Divide $x$ by $1$ .

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 4 x + 12 & x < \frac{12}{4} \end{cases}$

Divide $12$ by $4$ .

${\begin{cases} 4 x - 12 & x \geq 3 \\ - 4 x + 12 & x < 3 \end{cases}$

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