Absolute Value Equations and Inequalities
Math ⇒ Algebra
Absolute Value Equations and Inequalities starts at 9 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Absolute Value Equations and Inequalities.
How you perform is determined by your score and the time you take.
When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
See sample questions for grade 11
Describe the steps to solve an absolute value equation of the form |ax + b| = c.
Explain why the equation |x + 1| = -3 has no solution.
Explain why the equation |x| = 0 has only one solution.
If |ax + b| = c, where c > 0, how many solutions does the equation have?
If |x + 2| ≥ 3, what is the solution set for x?
If |x| < a, where a > 0, what is the solution set for x?
Solve for x: |2x + 3| = 11.
Solve for x: |5 - x| = 2.
A student claims that the solution to |x - 2| = 5 is only x = 7. Is the student correct?
If |x - 3| > 0, which value of x does NOT satisfy the inequality?
(1) 0
(2) 3
(3) 5
(4) -3
Which of the following is the correct solution to |x| ≥ 6?
(1) x > 6
(2) x < -6 or x > 6
(3) x < 6
(4) -6 < x < 6
Which of the following is the solution set for |x + 3| < 5?
(1) x < 2
(2) -8 < x < 2
(3) -2 < x < 8
(4) -5 < x < 2
Which of the following is the solution to |2x| < 8?
(1) -4 < x < 4
(2) -8 < x < 8
(3) x < 4
(4) x > -4
Fill in the blank: The absolute value of any real number is always _______ or positive.
Fill in the blank: The graph of y = |x| is a _______.
Fill in the blank: The solution to |x - 2| = 0 is x = _______.
A student claims that the solution to |x - 2| = 5 is only x = 7. Is the student correct?
True or False: The equation |x| = -4 has no solution.
True or False: The solution to |x - 1| ≥ 0 is all real numbers.
True or False: The solution to |x + 2| ≤ 0 is x = -2.
