Algebra Examples

$\frac{1}{x + 10} > 0$

Step 1

Solve $x > - 10$ .

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Step 1.1

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

$x + 10 = 0$

Step 1.2

Subtract $10$ from both sides of the equation.

$x = - 10$

Step 1.3

Find the domain of $\frac{1}{x + 10}$ .

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Step 1.3.1

Set the denominator in $\frac{1}{x + 10}$ equal to $0$ to find where the expression is undefined.

$x + 10 = 0$

Step 1.3.2

Subtract $10$ from both sides of the equation.

$x = - 10$

Step 1.3.3

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

$(- \infty, - 10) \cup (- 10, \infty)$

Step 1.4

The solution consists of all of the true intervals.

$x > - 10$

Step 2

Use the inequality $x > - 10$ to build the set notation.

${x | x > - 10}$

Step 3