<p> Solving Rational Inequalities</p><p>Rational inequalities can be solved using the same principles as polynomial inequalities. One method is to graph the related function and observe graph over different intervals.</p><p>Think about places where a rational function can change signs (+ve to –ve or vice-versa). This can occur around ______or ______.</p><p>Ex. </p><p>Notice where the function can only change from <0 to >0 or vice-versa </p><p>Therefore, if we set up intervals between the zeroes and the asymptotes, we can test to find whether the function is <0 or >0 on those intervals.</p><p>Ex. 1 Solve the following inequality.</p><p>4 First we must set this relative to zero and put it < 20 x - 3 into a form we are familiar with.</p><p>Now, we can define the related function and either graph (if asked to solve graphically), or start to look at intervals created by the zeroes and the vertical asymptotes (if asked to solve algebraically). Since this is asking for when the rational is <0, zeroes will not be solutions!</p><p>V.A. Zeroes</p><p>Therefore, there is a vertical asymptote at ______and a zero at ______Interval check: (Algebraic Solution)</p><p> x f(x) Solution Outcome ** Choose any x value in the given interval</p><p>Write final answer in 1 of the following ways:</p><p>Or</p><p> x 2 3x  4 Ex. 2 Solve:  0 Notice: Since this question is asking for when the related x 2  5x  6 rational function is  0, the zeroes will be solutions</p><p>Answers: 1) x ≤ 3 2) x ≥ -3 3) t > 20 4) p < -15 5) x < 0 or x ≥ 2/5 6) x ≤ -1 or x ≥ -5/6 7) x ≤ 13/5 or x > 3 8) y ≤ 20 9) x ≤ 15/8 or x >2 10) 0 < x ≤ ¾</p><p>11) or </p><p>12) -1 < x <1</p>