Precalculus Examples

$| 5 x - 5 |$

The piecewise polynomials are $5 x - 5$ when $5 x - 5 \geq 0$ and $(- 1) (5 x - 5)$ when $5 x - 5 < 0$ .

${\begin{cases} (5 x - 5) & 5 x - 5 \geq 0 \\ (- 1) (5 x - 5) & 5 x - 5 < 0 \end{cases}$

Remove parentheses.

${\begin{cases} 5 x - 5 & 5 x - 5 \geq 0 \\ (- 1) (5 x - 5) & 5 x - 5 < 0 \end{cases}$

Solve for $x$ when $5 x - 5 \geq 0$ .

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Since $- 5$ does not contain the variable to solve for, move it to the right side of the inequality by adding $5$ to both sides.

${\begin{cases} 5 x - 5 & 5 x \geq 5 \\ (- 1) (5 x - 5) & 5 x - 5 < 0 \end{cases}$

Divide each term by $5$ and simplify.

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Divide each term in $5 x \geq 5$ by $5$ .

${\begin{cases} 5 x - 5 & \frac{5 x}{5} \geq \frac{5}{5} \\ (- 1) (5 x - 5) & 5 x - 5 < 0 \end{cases}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

${\begin{cases} 5 x - 5 & \frac{5 x}{5} \geq \frac{5}{5} \\ (- 1) (5 x - 5) & 5 x - 5 < 0 \end{cases}$

Divide $x$ by $1$ to get $x$ .

${\begin{cases} 5 x - 5 & x \geq \frac{5}{5} \\ (- 1) (5 x - 5) & 5 x - 5 < 0 \end{cases}$

Divide $5$ by $5$ to get $1$ .

${\begin{cases} 5 x - 5 & x \geq 1 \\ (- 1) (5 x - 5) & 5 x - 5 < 0 \end{cases}$

Simplify $(- 1) (5 x - 5)$ .

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Apply the distributive property.

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 1 (5 x) - 1 \cdot - 5 & 5 x - 5 < 0 \end{cases}$

Multiply.

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Multiply $5$ by $- 1$ to get $- 5$ .

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 5 x - 1 \cdot - 5 & 5 x - 5 < 0 \end{cases}$

Multiply $- 1$ by $- 5$ to get $5$ .

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 5 x + 5 & 5 x - 5 < 0 \end{cases}$

Solve for $x$ when $5 x - 5 < 0$ .

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Since $- 5$ does not contain the variable to solve for, move it to the right side of the inequality by adding $5$ to both sides.

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 5 x + 5 & 5 x < 5 \end{cases}$

Divide each term by $5$ and simplify.

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Divide each term in $5 x < 5$ by $5$ .

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 5 x + 5 & \frac{5 x}{5} < \frac{5}{5} \end{cases}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 5 x + 5 & \frac{5 x}{5} < \frac{5}{5} \end{cases}$

Divide $x$ by $1$ to get $x$ .

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 5 x + 5 & x < \frac{5}{5} \end{cases}$

Divide $5$ by $5$ to get $1$ .

${\begin{cases} 5 x - 5 & x \geq 1 \\ - 5 x + 5 & x < 1 \end{cases}$

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Precalculus Examples

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