Algebra Examples

$\frac{1}{x + 4} > 0$

Step 1

Find all the values where the expression switches from negative to positive by setting each factor equal to $0$ and solving.

$x + 4 = 0$

Step 2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 3

Find the domain of $\frac{1}{x + 4}$ .

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Step 3.1

Set the denominator in $\frac{1}{x + 4}$ equal to $0$ to find where the expression is undefined.

$x + 4 = 0$

Step 3.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 3.3

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

$(- \infty, - 4) \cup (- 4, \infty)$

Step 4

The solution consists of all of the true intervals.

$x > - 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - 4$

Interval Notation:

$(- 4, \infty)$

Step 6