Absolute Value Inequalities

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the definition of absolute value?
Back
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.
2.
FLASHCARD QUESTION
Front
What does the inequality |x| < a represent?
Back
It represents all values of x that are within a distance a from 0 on the number line.
3.
FLASHCARD QUESTION
Front
What does the inequality |x| > a represent?
Back
It represents all values of x that are more than a distance a from 0 on the number line.
4.
FLASHCARD QUESTION
Front
How do you solve the inequality |x - 4| < 5?
Back
Split into two inequalities: -5 < x - 4 < 5, which simplifies to -1 < x < 9.
5.
FLASHCARD QUESTION
Front
How do you solve the inequality |x + 2| > 3?
Back
Split into two inequalities: x + 2 > 3 or x + 2 < -3, which simplifies to x > 1 or x < -5.
6.
FLASHCARD QUESTION
Front
What is the solution to |2x - 1| = 7?
Back
The solutions are x = -3 or x = 4.
7.
FLASHCARD QUESTION
Front
What is the solution to |x + 3| > -8?
Back
All real numbers are solutions because absolute values are always non-negative.
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