Absolute Value Inequalities
Flashcard
•
Mathematics
•
8th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an absolute value inequality?
Back
An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.
2.
FLASHCARD QUESTION
Front
What does the symbol |x| < a represent?
Back
The symbol |x| < a means that the value of x is within a distance of a from zero, resulting in the compound inequality -a < x < a.
3.
FLASHCARD QUESTION
Front
What does the symbol |x| > a represent?
Back
The symbol |x| > a means that the value of x is outside the distance of a from zero, resulting in the compound inequality x < -a or x > a.
4.
FLASHCARD QUESTION
Front
What is a compound inequality?
Back
A compound inequality is an inequality that combines two or more inequalities, often connected by the words 'and' or 'or'.
5.
FLASHCARD QUESTION
Front
What is the difference between 'and' and 'or' in compound inequalities?
Back
'And' indicates that both conditions must be true simultaneously, while 'or' indicates that at least one of the conditions must be true.
6.
FLASHCARD QUESTION
Front
How do you solve the inequality |x - 5| < 3?
Back
To solve |x - 5| < 3, you set up the compound inequality: -3 < x - 5 < 3, which simplifies to 2 < x < 8.
7.
FLASHCARD QUESTION
Front
How do you solve the inequality |2x + 1| > 4?
Back
To solve |2x + 1| > 4, you set up the compound inequalities: 2x + 1 < -4 or 2x + 1 > 4, which simplifies to x < -2.5 or x > 1.5.
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