Mathematics
Absolute Value Inequalities
An absolute value inequality involves expressions like |x + a| < b. It's critical for understanding distances and tolerances in equations. ScanSolve provides a clear breakdown of cases and interval testing.
How to Approach Absolute Value Inequalities
- 01
Input the Inequality
Enter or upload a photo of an absolute value inequality, such as |x - 3| ≥ 5.
- 02
Identify Critical Points
ScanSolve helps find critical points where the absolute value changes to zero, e.g., x - 3 = 5 and x - 3 = -5.
- 03
Test Intervals for Solution
Check intervals between critical points to determine where the inequality holds true and graph the solution accordingly.
Frequently Asked Questions
What are absolute value inequalities?
They compare the absolute value of an expression to a number, like |x + a| < b or |x - 2| ≥ 4.
How are solutions graphed?
Solutions are graphed on a number line, indicating intervals where the inequality holds.
Why test intervals?
Interval testing ensures each segment between critical points satisfies the inequality, verifying solutions.
Related Topics
More step-by-step guides in Mathematics and adjacent subjects.
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