Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
6. Solving Absolute Value Inequalities
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Exercise 21 Page 91

Error: Forgot to write the compound inequality
Correct Solution: -15

Practice makes perfect

Consider the given exercise.

Absolute Value Inequality Wrong
To solve absolute value inequalities we must write the given inequality as two separate cases. If we have an inequality of the form |x+a|non-negative number, we can write it as a compound inequality. x+a < b and x+a>- b Notice that in the work provided the second case was not considered. The student should have also solved x-5>- 20. Let's solve the inequality by correcting this mistake!
|x-5|<20

Rewrite as compound inequality

x-5 < 20 and x-5 > -20
-20 < x-5 < 20

Add 5 to each expression

-20 + 5 < x-5+5 < 20+5
-15 < x < 25