Solving Absolute Value Inequalities

What is the first step in solving an absolute value inequality?

• Isolate the absolute value

• Combine like terms

• Distribute the constants

• Factor the equation

How do you determine if an absolute value inequality is an 'and' statement?

• If it is equal to

• If it is greater than or greater than or equal to

• If it is less than or less than or equal to

• If it is not equal to

What should you do after isolating the absolute value in an inequality?

• Factor the equation

• Combine like terms

• Determine if it is an 'and' or 'or' statement

• Distribute the constants

What does it mean if an absolute value inequality is an 'or' statement?

• The solution is empty

• The solution is a single interval

• The solution is the intersection of two intervals

• The solution is the union of two intervals

In Example 1, what is the interval notation for the solution of |x - 5| ≥ 8?

• (-∞, -5] ∪ [5, ∞)

• (-∞, -8] ∪ [8, ∞)

• (-∞, -3) ∪ (13, ∞)

• (-∞, -3] ∪ [13, ∞)

What is the interval notation for the solution of |x - 5| ≥ 8?

• (-∞, -8] ∪ [8, ∞)

• (-∞, -3) ∪ (13, ∞)

• (-∞, -3] ∪ [13, ∞)

• (-∞, -5] ∪ [5, ∞)

In Example 2, what is the interval notation for the solution of |y - 9| < 9?

• (0, 18)

• [0, 18]

• [0, 9]

• (0, 9)

In Example 3, what is the simplified interval notation for the solution of |6y - 2| < 18?

• (-8/3, 10/3)

• (-8, 10)

• (-16/6, 20/6)

• (-4, 5)

In Example 4, why is there no solution for the inequality |x - 3| < -4?

• Because the absolute value cannot be greater than a negative number

• Because the absolute value cannot be less than a negative number

• Because the absolute value cannot be less than zero

• Because the absolute value cannot be equal to a negative number

In Example 5, what is the interval notation for the solution of |3z + 15| ≥ 0?

• (-∞, ∞)

• (-∞, 0)

• (-5, 5)

• (-15, 15)