Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig Review3.23x−2x− 11 > 0SolutionThis one is a little different, but not really more difficult. The quadratic doesn’tfactor and so we’ll need to use the quadratic formula to solve for where it is zero.Doing this gives1±34x =3Reducing to decimals this is x = 2.27698 and x = − 1.61032. From this point on it’sidentical to the previous two problems. In the number line below the dashed lines areat the approximate values of the two numbers above and the inequalities show thevalue of the quadratic evaluated at the test points shown.From the number line above we see that the solution is⎛1+34 ⎞⎜ , ∞3 ⎟.⎝ ⎠⎛ 1−34 ⎞⎜−∞,3 ⎟⎝ ⎠and4.x − 3 ≥ 0x + 2SolutionThe process for solving inequalities that involve rational functions is nearly identicalto solving inequalities that involve polynomials. Just like polynomial inequalities,rational inequalities can change sign where the rational expression is zero. However,they can also change sign at any point that produces a division by zero error in therational expression. A good example of this is the rational expression 1 x . Clearly,there is division by zero at x = 0 and to the right of x = 0 the expression is positiveand to the left of x = 0 the expression is negative.It’s also important to note that a rational expression will only be zero for values of xthat make the numerator zero.© 2006 Paul Dawkins 39http://tutorial.math.lamar.edu/terms.aspx