Find the Domain y=2 square root of 4x+6

$y = 2 \sqrt{4 x + 6}$

Step 1

Set the radicand in $\sqrt{4 x + 6}$ greater than or equal to $0$ to find where the expression is defined.

$4 x + 6 \geq 0$

Step 2

Solve for $x$ .

Subtract $6$ from both sides of the inequality.

$4 x \geq - 6$

Divide each term in $4 x \geq - 6$ by $4$ and simplify.

Divide each term in $4 x \geq - 6$ by $4$ .

$\frac{4 x}{4} \geq \frac{- 6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{- 6}{4}$

Divide $x$ by $1$ .

$x \geq \frac{- 6}{4}$

Simplify the right side.

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$x \geq \frac{2 (- 3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x \geq \frac{2 \cdot - 3}{2 \cdot 2}$

Cancel the common factor.

$x \geq \frac{2 \cdot - 3}{2 \cdot 2}$

Rewrite the expression.

$x \geq \frac{- 3}{2}$

Move the negative in front of the fraction.

$x \geq - \frac{3}{2}$

Step 3

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

Interval Notation:

$[- \frac{3}{2}, \infty)$

Set-Builder Notation:

${x | x \geq - \frac{3}{2}}$

Step 4