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

Algebra/Trig ReviewIn this case we won’t include any endpoints in the solution since they either givedivision by zero or make the expression zero and we want strictly less than zero forthis problem.The solution is then ( −∞, − 2) and (1, 5) .6.2x≥ 3x + 1SolutionWe need to be a little careful with this one. In this case we need to get zero on oneside of the inequality. This is easy enough to do. All we need to do is subtract 3 fromboth sides. This gives2x−3≥0x + 12x− 3( x+1)≥ 0x + 1−x−3≥ 0x + 1Notice that I also combined everything into a single rational expression. You willalways want to do this. If you don’t do this it can be difficult to determine where therational expression is zero. So once we’ve gotten it into a single expression it’s easyto see that the numerator will be zero at x = − 3 and the denominator will be zero atx = − 1. The number line for this problem is below.© 2006 Paul Dawkins 41http://tutorial.math.lamar.edu/terms.aspx