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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

01

Step 1. Given information.

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

02

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

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

03

Step 3. Simplified answer.

The domain of the given inequality is $(- 鈭�, - 2) 鈭� (- 2, 6) 鈭� (6, 鈭�)$ .

The solutions consists of all of the true intervals.

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

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