Solving Absolute Value Inequalities

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•
Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an absolute value inequality?
Back
An inequality that contains an absolute value expression, which measures the distance of a number from zero on the number line.
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, leading to x > 5 or x < -11.
3.
FLASHCARD QUESTION
Front
What does the solution x < -11 or x > 5 represent?
Back
It represents all values of x that are either less than -11 or greater than 5.
4.
FLASHCARD QUESTION
Front
What is the first step in solving | -8x | < 8?
Back
Separate into two inequalities with an 'and': -8x < 8 and -8x > -8.
5.
FLASHCARD QUESTION
Front
What is the solution to the inequality |x| < a?
Back
The solution is -a < x < a.
6.
FLASHCARD QUESTION
Front
What does the compound inequality m < -1 OR m > 2 indicate?
Back
It indicates that m can take any value less than -1 or any value greater than 2.
7.
FLASHCARD QUESTION
Front
How do you represent the solution n > 10 or n < -6 graphically?
Back
On a number line, shade the region to the right of 10 and the region to the left of -6.
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