Linear Algebra Examples

$\sqrt{4 x + 40} - 12 = 0$

Step 1

Set the radicand in $\sqrt{4 x + 40}$ greater than or equal to $0$ to find where the expression is defined.

$4 x + 40 \geq 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Subtract $40$ from both sides of the inequality.

$4 x \geq - 40$

Step 2.2

Divide each term in $4 x \geq - 40$ by $4$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $4 x \geq - 40$ by $4$ .

$\frac{4 x}{4} \geq \frac{- 40}{4}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{- 40}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 40}{4}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $- 40$ by $4$ .

$x \geq - 10$

Step 3

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

Interval Notation:

$[- 10, \infty)$

Set-Builder Notation:

${x | x \geq - 10}$

Step 4