Precalculus Examples

$| 2 x + 4 |$

The piecewise polynomials are $2 x + 4$ when $2 x + 4 \geq 0$ and $(- 1) (2 x + 4)$ when $2 x + 4 < 0$ .

${\begin{cases} (2 x + 4) & 2 x + 4 \geq 0 \\ (- 1) (2 x + 4) & 2 x + 4 < 0 \end{cases}$

Remove parentheses.

${\begin{cases} 2 x + 4 & 2 x + 4 \geq 0 \\ (- 1) (2 x + 4) & 2 x + 4 < 0 \end{cases}$

Solve for $x$ when $2 x + 4 \geq 0$ .

Tap for more steps...

Subtract $4$ from both sides of the inequality.

${\begin{cases} 2 x + 4 & 2 x \geq - 4 \\ (- 1) (2 x + 4) & 2 x + 4 < 0 \end{cases}$

Divide each term by $2$ and simplify.

Tap for more steps...

Divide each term in $2 x \geq - 4$ by $2$ .

${\begin{cases} 2 x + 4 & \frac{2 x}{2} \geq \frac{- 4}{2} \\ (- 1) (2 x + 4) & 2 x + 4 < 0 \end{cases}$

Reduce the expression by cancelling the common factors.

Tap for more steps...

Cancel the common factor.

${\begin{cases} 2 x + 4 & \frac{2 x}{2} \geq \frac{- 4}{2} \\ (- 1) (2 x + 4) & 2 x + 4 < 0 \end{cases}$

Divide $x$ by $1$ .

${\begin{cases} 2 x + 4 & x \geq \frac{- 4}{2} \\ (- 1) (2 x + 4) & 2 x + 4 < 0 \end{cases}$

Divide $- 4$ by $2$ .

${\begin{cases} 2 x + 4 & x \geq - 2 \\ (- 1) (2 x + 4) & 2 x + 4 < 0 \end{cases}$

Simplify $(- 1) (2 x + 4)$ .

Tap for more steps...

Apply the distributive property.

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 1 (2 x) - 1 \cdot 4 & 2 x + 4 < 0 \end{cases}$

Multiply.

Tap for more steps...

Multiply $2$ by $- 1$ .

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 2 x - 1 \cdot 4 & 2 x + 4 < 0 \end{cases}$

Multiply $- 1$ by $4$ .

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 2 x - 4 & 2 x + 4 < 0 \end{cases}$

Solve for $x$ when $2 x + 4 < 0$ .

Tap for more steps...

Subtract $4$ from both sides of the inequality.

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 2 x - 4 & 2 x < - 4 \end{cases}$

Divide each term by $2$ and simplify.

Tap for more steps...

Divide each term in $2 x < - 4$ by $2$ .

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 2 x - 4 & \frac{2 x}{2} < \frac{- 4}{2} \end{cases}$

Reduce the expression by cancelling the common factors.

Tap for more steps...

Cancel the common factor.

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 2 x - 4 & \frac{2 x}{2} < \frac{- 4}{2} \end{cases}$

Divide $x$ by $1$ .

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 2 x - 4 & x < \frac{- 4}{2} \end{cases}$

Divide $- 4$ by $2$ .

${\begin{cases} 2 x + 4 & x \geq - 2 \\ - 2 x - 4 & x < - 2 \end{cases}$

Enter YOUR Problem