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Section 2.15 : Absolute Value Inequalities
6. Solve the following equation.
\[\left| {10 - 3w} \right| \ge 4\]Show All Steps Hide All Steps
Start SolutionThere really isn’t all that much to this problem. All we need to do is use the formula for “greater than” inequalities we discussed in the notes for this section. Doing that gives,
\[10 - 3w \le - 4\hspace{0.25in}{\mbox{or}}\hspace{0.25in}10 - 3w \ge 4\] Show Step 2To get the solution all we need to do then is solve the two inequalities from the previous step. Here is that work.
\[\begin{array}{c}10 - 3w \le - 4\hspace{0.25in}{\mbox{or}}\hspace{0.25in}10 - 3w \ge 4\\ - 3w \le - 14\hspace{0.25in}{\mbox{or}}\hspace{0.25in} - 3w \ge - 6\\ \displaystyle \require{bbox} \bbox[2pt,border:1px solid black]{{w \ge \frac{{14}}{3}\hspace{0.25in}{\mbox{or}}\hspace{0.25in}\hspace{0.25in}w \le 2}}\end{array}\]Remember that when dividing all parts of an inequality by a negative number (as we did here) we need to also switch the direction of the inequalities!