Finite Math Examples Equations and Inequalities

Find the Domain

$\sqrt{3 x + 9}$

Step 1

Set the radicand in $\sqrt{3 x + 9}$ greater than or equal to $0$ to find where the expression is defined.

$3 x + 9 \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $9$ from both sides of the inequality.

$3 x \geq - 9$

Step 2.2

Divide each term in $3 x \geq - 9$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x \geq - 9$ by $3$ .

$\frac{3 x}{3} \geq \frac{- 9}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{- 9}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 9}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 9$ by $3$ .

$x \geq - 3$

Step 3

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

Interval Notation:

$[- 3, \infty)$

Set-Builder Notation:

${x | x \geq - 3}$

Step 4

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Find the Domain

Equations and Inequalities

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