Inequalities with Absolute Value
Math ⇒ Algebra
Inequalities with Absolute Value starts at 8 and continues till grade 12.
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See sample questions for grade 9
A temperature sensor records the difference between the current temperature and 25°C as |T - 25| ≤ 3. What is the possible range of temperatures T?
Explain the general method for solving inequalities involving absolute value.
If |2x - 4| < 6, what is the solution set for x?
If |x - 2| ≤ 0, what is the value of x?
If |x + 2| > 5, what is the solution set for x?
If |x| < a, where a > 0, what is the solution set for x?
If |x| > a, where a > 0, what is the solution set for x?
A temperature sensor records the difference between the current temperature and 25°C as |T - 25| ≤ 3. What is the possible range of temperatures T?
Which of the following is a solution to |2x - 1| > 7?
(1) x = 5
(2) x = 3
(3) x = -4
(4) x = 0
Which of the following is NOT a solution to |x - 2| ≤ 3?
(1) x = 5
(2) x = -1
(3) x = 6
(4) x = 2
Which of the following is NOT a solution to |x + 4| ≥ 4?
(1) x = 0
(2) x = -8
(3) x = 1
(4) x = 4
Which of the following is NOT a solution to |x| > 2?
(1) x = 3
(2) x = -3
(3) x = 2
(4) x = -5
Fill in the blank: The solution to |2x| < 8 is ________ < x < ________.
Fill in the blank: The solution to |x - 2| = 0 is x = ________.
Fill in the blank: The solution to |x - 3| < 1 is ________ < x < ________.
Fill in the blank: The solution to |x - 7| > 0 is all real numbers except x = ________.
True or False: The inequality |x| ≥ 0 is true for all real numbers.
True or False: The solution to |x - 1| ≥ 0 is all real numbers.
True or False: The solution to |x - 5| < 0 is the empty set.
True or False: The solution to |x + 1| ≤ -2 is the empty set.
