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Section 2.15 : Absolute Value Inequalities

5. Solve the following equation.

\[\left| {2z - 7} \right| > 1\]

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Start Solution

There 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,

\[2z - 7 < - 1\hspace{0.25in}{\mbox{or}}\hspace{0.25in}2z - 7 > 1\] Show Step 2

To get the solution all we need to do then is solve the two inequalities from the previous step. Here is that work.

\[\begin{array}{c}2z - 7 < - 1\hspace{0.25in}{\mbox{or}}\hspace{0.25in}2z - 7 > 1\\ 2z < 6\hspace{0.25in}{\mbox{or}}\hspace{0.25in}2z > 8\\ \require{bbox} \bbox[2pt,border:1px solid black]{{z < 3\hspace{0.25in}{\mbox{or}}\hspace{0.25in}\hspace{0.25in}z > 4}}\end{array}\]