Algebra Examples

$| 8 x + 8 |$

The piecewise polynomials are $8 x + 8$ when $8 x + 8 \geq 0$ and $(- 1) (8 x + 8)$ when $8 x + 8 < 0$ .

${\begin{cases} (8 x + 8) & 8 x + 8 \geq 0 \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Remove parentheses.

${\begin{cases} 8 x + 8 & 8 x + 8 \geq 0 \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Solve for $x$ when $8 x + 8 \geq 0$ .

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Subtract $8$ from both sides of the inequality.

${\begin{cases} 8 x + 8 & 8 x \geq - 8 \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Divide each term by $8$ and simplify.

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Divide each term in $8 x \geq - 8$ by $8$ .

${\begin{cases} 8 x + 8 & \frac{8 x}{8} \geq - \frac{8}{8} \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

${\begin{cases} 8 x + 8 & \frac{8 x}{8} \geq - \frac{8}{8} \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Divide $x$ by $1$ .

${\begin{cases} 8 x + 8 & x \geq - \frac{8}{8} \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Simplify the right side of the equation.

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Divide $8$ by $8$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \cdot 1 \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Multiply $- 1$ by $1$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \\ (- 1) (8 x + 8) & 8 x + 8 < 0 \end{cases}$

Simplify $(- 1) (8 x + 8)$ .

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Apply the distributive property.

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 1 (8 x) - 1 \cdot 8 & 8 x + 8 < 0 \end{cases}$

Multiply.

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Multiply $8$ by $- 1$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 1 \cdot 8 & 8 x + 8 < 0 \end{cases}$

Multiply $- 1$ by $8$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 8 & 8 x + 8 < 0 \end{cases}$

Solve for $x$ when $8 x + 8 < 0$ .

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Subtract $8$ from both sides of the inequality.

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 8 & 8 x < - 8 \end{cases}$

Divide each term by $8$ and simplify.

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Divide each term in $8 x < - 8$ by $8$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 8 & \frac{8 x}{8} < - \frac{8}{8} \end{cases}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 8 & \frac{8 x}{8} < - \frac{8}{8} \end{cases}$

Divide $x$ by $1$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 8 & x < - \frac{8}{8} \end{cases}$

Simplify the right side of the equation.

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Divide $8$ by $8$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 8 & x < - 1 \cdot 1 \end{cases}$

Multiply $- 1$ by $1$ .

${\begin{cases} 8 x + 8 & x \geq - 1 \\ - 8 x - 8 & x < - 1 \end{cases}$

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