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

Algebra/Trig ReviewSolutionThis one works identically to the previous problem.2x− 4 = 10 2x− 4 =−102x= 14 OR 2x= −6x= 7 x= −3Do not make the following very common mistake in solve absolute value equationsand inequalities.2x−4 ≠ 2x+ 4 = 102x= 6x = 3Did you catch the mistake? In dropping the absolute value bars I just changed every“-” into a “+” and we know that doesn’t work that way! By doing this we get a singleanswer and it’s incorrect as well. Simply plug it into the original equation toconvince yourself that it’s incorrect.2( 3)− 4 = 6 − 4 = 2 = 2 ≠ 10When first learning to solve absolute value equations and inequalities people tend tojust convert all minus signs to plus signs and solve. This is simply incorrect and willalmost never get the correct answer. The way to solve absolute value equations is theway that I’ve shown here.3. x + 1 =− 15SolutionThis question is designed to make sure you understand absolute values. In this casewe are after the values of x such that when we plug them into x + 1 we will get -15.This is a problem however. Recall that absolute value ALWAYS returns a positivenumber! In other words, there is no way that we can get -15 out of this absolutevalue. Therefore, there are no solutions to this equation.4. 7x −10 ≤ 4SolutionTo solve absolute value inequalities with < or ≤ in them we usep < d ⇒ − d < p