An absolute value inequality that has a solution set -1<=x<=3 is |x-1| <= 2
What is the solution set for an inequality?
The set of values of the variable involved in the inequality for which the considered inequality holds true is called the solution set for that inequality.
We've to find an absolute value inequality that has the solution set
-1 <= x <= 3
1+2 = 3
and 1 - 2 = 3
Therefore, we can rewrite the considered inequality as:
1-2 <= x <1+2
Subtracting 1 from all the sides:
-2 <= x-1 <= 2
This is written as:
|x-1| <= 2 (it is because [tex]|x| \leq a \leftrightarrow-a \leq x \leq a[/tex] )
Thus, an absolute value inequality that has a solution set -1<=x<=3 is |x-1| <= 2
Learn more about absolute value inequality here:
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