Find the Domain square root of 6+7x

$\sqrt{6 + 7 x}$

Step 1

Set the radicand in $\sqrt{6 + 7 x}$ greater than or equal to $0$ to find where the expression is defined.

$6 + 7 x \geq 0$

Step 2

Solve for $x$ .

Subtract $6$ from both sides of the inequality.

$7 x \geq - 6$

Divide each term in $7 x \geq - 6$ by $7$ and simplify.

Divide each term in $7 x \geq - 6$ by $7$ .

$\frac{7 x}{7} \geq \frac{- 6}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} \geq \frac{- 6}{7}$

Divide $x$ by $1$ .

$x \geq \frac{- 6}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x \geq - \frac{6}{7}$

Step 3

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

Interval Notation:

$[- \frac{6}{7}, \infty)$

Set-Builder Notation:

${x | x \geq - \frac{6}{7}}$

Step 4