Solving Absolute Value Inequalities

The video tutorial covers absolute value inequalities, explaining how to solve them when the absolute value is less than or greater than a number. It includes examples and tests points to determine the solution set. The tutorial also demonstrates graphing solutions and discusses the importance of understanding the pattern in solving these inequalities.

What does the absolute value of a number represent?

• The negative of the number

• The square of the number

• The distance from zero

• The number itself

If |x| < 3, which of the following is true?

• x can be 5

• x can be 2

• x can be 4

• x can be -4

For the inequality |x| > 3, which of the following is a solution?

• x = 2

• x = -2

• x = 0

• x = 4

Which of the following points would NOT be shaded for |x| > 3?

• x = 4

• x = 0

• x = -7

• x = 5

What is the first step in solving the inequality |5x - 2| < 3?

• Add 2 to both sides

• Divide by 5

• Split the inequality into two

• Subtract 2 from both sides

After splitting the inequality |5x - 2| < 3, what are the two resulting inequalities?

• 5x - 2 > 3 and 5x - 2 > -3

• 5x - 2 > 3 and 5x - 2 < -3

• 5x - 2 < 3 and 5x - 2 > -3

• 5x - 2 < 3 and 5x - 2 < -3

When graphing the solution to |5x - 2| < 3, what type of circles are used at the boundary points?

• No circles

• Closed circles

• Half-filled circles

• Open circles

Which point would be shaded for the inequality |5x - 2| < 3?

• x = -3

• x = 4

• x = 0

• x = 2

In the inequality 3|x + 6| - 8 ≥ 4, what is the first step to isolate the absolute value?

• Subtract 8 from both sides

• Multiply by 3

• Add 8 to both sides

• Divide by 3

For the inequality 3|x + 6| - 8 ≥ 4, what is the solution set?

• x ≤ -10 or x ≥ -2

• x ≥ -10 or x ≤ -2

• x ≤ -2 or x ≥ -10

• x ≥ -2 or x ≤ -10