Absolute Value Equations and Inequalities

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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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 equation y = -|x| + 4 represent graphically?
Back
It represents a V-shaped graph that opens downwards, reflecting across the x-axis and shifted up 4 units.
3.
FLASHCARD QUESTION
Front
What is the solution set for the inequality |x - 3| < 5?
Back
The solution set is 3 - 5 < x < 3 + 5, which simplifies to -2 < x < 8.
4.
FLASHCARD QUESTION
Front
Can an absolute value equal a negative number?
Back
No, an absolute value cannot equal a negative number.
5.
FLASHCARD QUESTION
Front
What is the general form of an absolute value equation?
Back
The general form is |x - a| = b, where a is a constant and b is a non-negative number.
6.
FLASHCARD QUESTION
Front
How do you solve the equation |x + 4| = 7?
Back
Split into two cases: x + 4 = 7 and x + 4 = -7. Solutions are x = 3 and x = -11.
7.
FLASHCARD QUESTION
Front
What does the inequality |x + 2| > 5 mean?
Back
It means that x is either less than -3 or greater than 3.
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