Precalculus Examples

$\sqrt{- 3 (1 - 5 x)}$

Step 1

Set the radicand in $\sqrt{- 3 (1 - 5 x)}$ greater than or equal to $0$ to find where the expression is defined.

$- 3 (1 - 5 x) \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $- 3 (1 - 5 x) \geq 0$ by $- 3$ and simplify.

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Step 2.1.1

Divide each term in $- 3 (1 - 5 x) \geq 0$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 (1 - 5 x)}{- 3} \leq \frac{0}{- 3}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $- 3$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{- 3 (1 - 5 x)}{- 3} \leq \frac{0}{- 3}$

Step 2.1.2.1.2

Divide $1 - 5 x$ by $1$ .

$1 - 5 x \leq \frac{0}{- 3}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $- 3$ .

$1 - 5 x \leq 0$

Step 2.2

Subtract $1$ from both sides of the inequality.

$- 5 x \leq - 1$

Step 2.3

Divide each term in $- 5 x \leq - 1$ by $- 5$ and simplify.

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Step 2.3.1

Divide each term in $- 5 x \leq - 1$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \geq \frac{- 1}{- 5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} \geq \frac{- 1}{- 5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 1}{- 5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Dividing two negative values results in a positive value.

$x \geq \frac{1}{5}$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[\frac{1}{5}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{1}{5}}$

Step 4