# solving absolute value inequalities template

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in this inequality, they’re asking me to find all the x-values that are less than three units away from zero in either direction, so the solution is going to be the set of all the points that are less than three units away from zero. in other words, all the points between –3 and 3, but not actually including –3 or 3, will work as solutions to this inequality. since this is a “less than” absolute-value inequality, my first step is to clear the absolute value according to the “less than” pattern. even –2 will not work, and neither will +2 (although they’re right on the edge), because this is a “greater than” (but not equal to) inequality.

the solution to this “greater than” absolute-value inequality is two regular inequalities, not one. because the variable cannot be in both of the solution intervals and the same time. so i can convert my last line above to the following: what they’ve given me is in two pieces, joined with an “or”, so i know that this will be a “greater than” absolute-value inequality. half of five is 2.5. so i want to adjust the inequality so it relates to –2.5 and +2.5, instead of relating to +19 and +24. they’re asking you for the x-values that will make the absolute-value expression greater than a negative number.

solving absolute value equations and inequalities. and represents the distance between a and 0 on a number line. has two solutions x = a and x = -a because both numbers are at the distance a from 0. you begin by making it into two separate equations and then solving them separately. inequalities that include absolute-value expressions can feel complicated. however, with some logic and a little as we will see the process for solving inequalities with a example 1 solve each of the following., solving absolute value inequalities worksheet, solving absolute value inequalities worksheet, solving absolute value inequalities calculator, absolute value inequalities rules, absolute value inequalities problems.

example 1: solve the absolute value inequality . |x+3| < -2. if you're not familiar yet with the different cases, i suggest that remember that an absolute value cannot be a negative number. example . solve: | this statement is never true, so there is no solution to this problem. example 4: | 3x – 4| + 9 > 5. step 1: isolate the absolute , how to solve inequalities with absolute values on both sides, absolute value inequalities examples, absolute value inequalities examples, double absolute value inequalities, solving absolute value inequalities graphically

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