Chapter 11: Q.476. (page 1069)

Solve the rational inequality and write the solution in interval notation.
$\frac{1}{x^{2} - 4 x - 12} < 0$

Short Answer

Expert verified

The solution is $- 2 < x < 6$ or $(- 2, 6)$ .

Step by step solution

Step 1. Given information.

The given inequality is $\frac{1}{x^{2} - 4 x - 12} < 0$ .

Step 2. Find all the values where the expression switches from negative to positive by setting each factor equal to zero.

$\begin{array}{rcl} x^{2} - 4 x - 12 & = & 0 \\ x^{2} - 6 x + 2 x - 12 & = & 0 \\ x (x - 6) + 2 (x - 6) & = & 0 \\ (x - 6) (x + 2) & = & 0 \\ \Rightarrow & x = 6 o r x = - 2 \end{array}$

Step 3. Simplified answer.

The domain of the given inequality is $(- \infty, - 2) \cup (- 2, 6) \cup (6, \infty)$ .

The solutions consists of all of the true intervals.

$- 2 < x < 6$ or $(- 2, 6)$

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Solve the rational inequality and write the solution in interval notation.
$\frac{1}{x^{2} - 4 x - 12} < 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find all the values where the expression switches from negative to positive by setting each factor equal to zero.

Step 3. Simplified answer.

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Solve the rational inequality and write the solution in interval notation.1x2-4x-12<0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find all the values where the expression switches from negative to positive by setting each factor equal to zero.

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Solve the rational inequality and write the solution in interval notation.
$\frac{1}{x^{2} - 4 x - 12} < 0$