Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Problem Solving - Page 58: 81


for the elephant: $|x-6008|\leq5992$ for the mouse: $|x-46000|\leq45000$

Work Step by Step

If $a\leq x\leq b$, we can turn this into an absolute value inequality in the following way: Take the mean of $a$ and $b$: $\frac{a+b}{2}$. This will be equidistant from $a$ and $b$. Thus if we take x's difference from this, it must be within $|a-\frac{a+b}{2}|=|b-\frac{a+b}{2}|$. Thus the inequality will be: $|x-\frac{a+b}{2}|\leq|a-\frac{a+b}{2}|$. Hence here the inequalities are: for the elephant: $|x-\frac{16+12000}{2}|\leq|16-\frac{16+12000}{2}|\\|x-6008|\leq5992$ for the mouse: $|x-\frac{1000+91000}{2}|\leq|1000-\frac{1000+91000}{2}|\\|x-46000|\leq45000$
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