Precalculus Examples

$| 4 x - 3 |$

The piecewise polynomials are $4 x - 3$ when $4 x - 3 \geq 0$ and $(- 1) (4 x - 3)$ when $4 x - 3 < 0$ .

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

Remove parentheses.

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

Solve for $x$ when $4 x - 3 \geq 0$ .

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Add $3$ to both sides of the inequality.

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

Divide each term by $4$ and simplify.

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Divide each term in $4 x \geq 3$ by $4$ .

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

Cancel the common factor of $4$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify $(- 1) (4 x - 3)$ .

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Apply the distributive property.

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

Multiply.

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Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $- 3$ .

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

Solve for $x$ when $4 x - 3 < 0$ .

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Add $3$ to both sides of the inequality.

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

Divide each term by $4$ and simplify.

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Divide each term in $4 x < 3$ by $4$ .

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

Cancel the common factor of $4$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

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