Pre-Algebra Examples

$\frac{- 2}{x - 10} < 0$

Step 1

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

$- 2 = 0$

$x - 10 = 0$

Step 2

Since $- 2 \neq 0$ , there are no solutions.

No solution

Step 3

Add $10$ to both sides of the equation.

$x = 10$

Step 4

Find the domain of $\frac{- 2}{x - 10}$ .

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Step 4.1

Set the denominator in $\frac{- 2}{x - 10}$ equal to $0$ to find where the expression is undefined.

$x - 10 = 0$

Step 4.2

Add $10$ to both sides of the equation.

$x = 10$

Step 4.3

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

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

Step 5

The solution consists of all of the true intervals.

$x > 10$

Step 6