Solving Absolute Value Inequalities Mastery

What does the absolute value of a number represent?

• The square of the number

• The negative of the number

• The distance from zero

• The number itself

If the absolute value of a is less than B, where does a lie on the number line?

• Greater than B

• Between -B and B

• Less than -B

• Equal to zero

How can the inequality |a| < B be rewritten without absolute values?

• -B < a < B

• a > B

• a < -B

• a = B

What does it mean if the absolute value of a is greater than B?

• a is equal to zero

• a is greater than B or less than -B

• a is between -B and B

• a is less than B

How can the inequality |a| > B be rewritten without absolute values?

• -B < a < B

• a > B or a < -B

• a = B

• a < B

In the example |3x + 1| ≥ 7, what are the two inequalities that can be derived?

• 3x + 1 = 7 and 3x + 1 = -7

• 3x + 1 ≥ 7 and 3x + 1 ≤ -7

• 3x + 1 > 7 and 3x + 1 < -7

• 3x + 1 < 7 and 3x + 1 > -7

What is the solution to the inequality 3x + 1 ≥ 7?

• x ≤ -3

• x ≥ 2

• x ≤ -2

• x ≥ 3

In the example |6x + 4| < 1, what is the resulting compound inequality?

• 6x + 4 = 1

• 6x + 4 < -1

• -1 < 6x + 4 < 1

• 6x + 4 > 1

What is the solution to the inequality -1 < 6x + 4 < 1?

• x = 0

• x < -1

• x > 1

• -5/6 < x < -1/2

What does the solution -5/6 < x < -1/2 mean in the context of the inequality |6x + 4| < 1?

• Any x outside this interval will satisfy the inequality

• No x will satisfy the inequality

• Any x in this interval will satisfy the inequality

• Only x = 0 will satisfy the inequality