Algebra Examples

$y = 3 \sqrt{6 x + 42}$

Step 1

Set the radicand in $\sqrt{6 x + 42}$ greater than or equal to $0$ to find where the expression is defined.

$6 x + 42 \geq 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $42$ from both sides of the inequality.

$6 x \geq - 42$

Step 2.2

Divide each term in $6 x \geq - 42$ by $6$ and simplify.

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Step 2.2.1

Divide each term in $6 x \geq - 42$ by $6$ .

$\frac{6 x}{6} \geq \frac{- 42}{6}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $6$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} \geq \frac{- 42}{6}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 42}{6}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 42$ by $6$ .

$x \geq - 7$

Step 3

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

Interval Notation:

$[- 7, \infty)$

Set-Builder Notation:

${x | x \geq - 7}$

Step 4