Exploring Absolute Value Inequalities

What does it mean if the absolute value of u is less than a?

• u is greater than a

• u is between -a and a

• u is equal to a

• u is less than -a

How do you convert an absolute value inequality with a 'less than' symbol?

• By converting it into a double-sided inequality

• By adding the absolute value symbols

• By multiplying both sides by -1

• By dividing both sides by 2

What intervals does u belong to if the absolute value of u is greater than a?

• Between 0 and a

• Between -infinity and -a or a and infinity

• Between -a and a

• Between -a and 0

What is the first step in solving the inequality |x - 4| < 8?

• Multiply both sides by 2

• Drop the absolute value symbols

• Add 4 to both sides

• Subtract 4 from both sides

What is the interval notation for the solution of |x - 4| < 8?

• (-4, 12)

• [-4, 12]

• (-4, 12]

• [4, 12)

How do you handle the inequality |3x - 2| ≥ 5?

• Subtract 2 from both sides

• Multiply both sides by 3

• Split it into two separate inequalities

• Convert it into a double-sided inequality

What is the first inequality when solving |3x - 2| ≥ 5?

• 3x + 2 ≥ 5

• 3x + 2 ≤ 5

• 3x - 2 ≥ 5

• 3x - 2 ≤ 5

What is the second inequality when solving |3x - 2| ≥ 5?

• 3x - 2 ≥ -5

• 3x - 2 ≤ -5

• 3x + 2 ≥ -5

• 3x + 2 ≤ -5

What is the interval notation for the solution of 3x - 2 ≤ -5?

• (-infinity, 1)

• (-infinity, -1]

• (-infinity, -1)

• (-infinity, 1]

What is the interval notation for the solution of 3x - 2 ≥ 5?

• (7/3, infinity)

• [7/3, infinity)

• [7/3, infinity]

• (7/3, infinity]