College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.6 - Page 420: 1

Answer

Solution set: $ (-\infty, -2)\cup(4,\infty)$

Work Step by Step

Follow the "Procedure for Solving Polynomial lnequalities",\ p.412: 1. Express the inequality in the form $f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$ where $f$ is a polynomial function. $f(x)=(x-4)(x+2)>0$ 2. Solve the equation $f(x)=0$. The real solutions are the boundary points. $(x-4)(x+2)=0$ $x=4$ or $x=-2$ 3. Locate these boundary points on a number line, thereby dividing the number line into intervals. 4. Test each interval's sign of $f(x)$ with a test value, $\left[\begin{array}{llll} Intervals: & (-\infty, -2) & (-2,4) & (4,\infty)\\ a=test.value & -10 & 0 & 10\\ f(a) & (-14)(-8) & (-4)(2) & (6)(12)\\ f(a) > 0 ? & T & F & T \end{array}\right]$ 5. Write the solution set, selecting the interval or intervals that satisfy the given inequality. If the inequality involves $\leq$ or $\geq$, include the boundary points. Solution set: $ (-\infty, -2)\cup(4,\infty)$
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