Absolute Value Inequalities

Flashcard
•
Mathematics
•
8th - 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
How do you solve the inequality |x + 3| > 8?
Back
Separate into two inequalities: x + 3 > 8 or x + 3 < -8, which simplifies to x > 5 or x < -11.
3.
FLASHCARD QUESTION
Front
What does the inequality | -8x | < 8 represent?
Back
It represents the values of x that are within 8 units of 0, leading to -8 < -8x < 8.
4.
FLASHCARD QUESTION
Front
What is a compound inequality?
Back
A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.
5.
FLASHCARD QUESTION
Front
How do you represent the solution to |x - 4| ≤ 5?
Back
The solution is -1 ≤ x ≤ 9, meaning x is between -1 and 9, inclusive.
6.
FLASHCARD QUESTION
Front
What is the first step in solving |x + 2| < 6?
Back
Separate into two inequalities: x + 2 < 6 and x + 2 > -6.
7.
FLASHCARD QUESTION
Front
What does the solution r ≥ -38 and r ≤ 32 mean?
Back
It means r can take any value from -38 to 32, including the endpoints.
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