Absolute Value Equations and Inequalities

Front

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.

Back

I, II, and III.

Front

Solution set of the equation |x + 2| = 7? Options: {-9, 5}, {-5, 9}, [-9,5], (-5,9)

Back

{-9, 5}

Front

Which mathematical sentence is represented by the given graph? Options:

x ≥ 2

,

|x| = 2

,

|x| > 2

,

|x| = ±2

Back

|x| = 2

Front

Sum of solutions of |x - 7| + 1 = 3?

Back

14

Front

Which absolute-value inequality corresponds to –2 < x < 4?

Back

|x - 1| < 3

Front

For any algebraic expression χ, and any positive real number a, which statement is NOT TRUE? Options:

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

Back

If |χ| ≥ α, then, -α ≥ χ ≥ α

Front

Which compound inequalities represent | 2x – 3 | > 5?

Back

2x - 3 > 5 or 2x - 3 < -5

Front

Solution set of the inequality | x – 3 | < 0?

Back

{ }

Front

For any algebraic expression X, which statement is NOT TRUE? Options:

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 (−∞, ∞).

Back

The solution set of |x| > 0 is (−∞, ∞).

Front

What is the solution set of the AVI | x – 5 | > -8?

Back

(−∞,∞)