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WorksheetsAbsolute Value Equations and Inequalities
Total questions: 10
Worksheet time: 8mins
Which of the following statements is TRUE?
I. The absolute value of a number is its distance from 0 on the number line.
II. Absolute values are always greater than or equal to zero.
III. For any algebraic expression X, and any positive real number a, if |X| = a, then X = a or X = -a.
I and II only.
I and III only.
II and III only.
I, II, and III.
Which of the following is the solution set of the AVE |x + 2| = 7?
{-9, 5}
{-5, 9}
[-9,5]
(-5,9)
Which of the following mathematical sentences is represented by the given graph?
x ≥ 2
|x| = 2
|x| > 2
|x| = ±2
What is the sum of the solutions of the AVE |x - 7| + 1 = 3?
10
12
14
16
Which of the following absolute-value inequality corresponds to –2 < x < 4?
|x| < 4
|x| > -2
|x| < 2
|x - 1| < 3
For any algebraic expression χ, and any positive real number a, which of the following is NOT TRUE?
If |χ| < α, then, -α < χ < α
If |χ| ≤ α, then, -α ≤ χ ≤ α
If |χ| ≥ α, then, -α ≥ χ ≥ α
If |χ| > α, then, χ > α or χ < -α
Which of the following compound inequalities represents the AVI | 2x – 3 | > 5, when split into compound inequalities?
-5 < 2x - 3 < 5
-5 > 2x - 3 > 5
2x - 3 > 5 or 2x - 3 < -5
2x - 3 > ± 5
What is the solution set of the AVI | x – 3 | < 0?
(−∞,∞)
{ }
{3}
(−∞,3) ∪ (3,∞)
For any algebraic expression X, which of the following statements is NOT TRUE?
The solution set of |x| > -1 is (−∞, ∞).
The solution set of |x| < -1 is { }.
The solution set of |x| ≤ 0 is { 0 }.
The solution set of |x| > 0 is (−∞, ∞).
What is the solution set of the AVI | x – 5 | > -8?
(−∞,∞)
{ }
{-3, 13}
(−∞,-3) ∪ (13,∞)
