Solving Absolute Value Inequalities

This video tutorial covers solving absolute value inequalities, focusing on both 'less than' and 'greater than' cases. It explains how to handle these inequalities by converting them into compound inequalities, using 'and' for less than and 'or' for greater than. The tutorial includes examples for each type, demonstrating the process of solving, graphing, and writing solutions in interval notation. The video concludes with additional examples to reinforce the concepts.

What is the main focus of learning target 3c?

• Solving quadratic equations

• Solving systems of equations

• Solving linear equations

• Solving absolute value equations and inequalities

How do you solve an absolute value inequality of the form |x| < a?

• By solving two separate inequalities

• By solving a compound inequality

• By solving a quadratic equation

• By solving a linear equation

In the inequality |x - 13| < 5, what is the equivalent compound inequality?

• -5 > x - 13 > 5

• x - 13 < 5

• x - 13 > -5

• -5 < x - 13 < 5

When solving |x| > a, what type of statement is used?

• A 'but' statement

• An 'and' statement

• A 'nor' statement

• An 'or' statement

What happens to the inequality sign when you multiply or divide by a negative number?

• It stays the same

• It flips

• It becomes an equality

• It becomes undefined

In the inequality |8x| ≥ 24, what are the two resulting inequalities?

• 8x > 24 and 8x < -24

• 8x < 24 and 8x > -24

• 8x ≤ 24 and 8x ≥ -24

• 8x ≥ 24 and 8x ≤ -24

What is the interval notation for the solution of |8x| ≥ 24?

• (-3, 3)

• (-∞, -3] ∪ [3, ∞)

• (-∞, -3) ∪ (3, ∞)

• (-3, 3]

In the inequality |3b - 7| > 28, what are the two resulting inequalities?

• 3b - 7 ≤ 28 and 3b - 7 ≥ -28

• 3b - 7 ≥ 28 and 3b - 7 ≤ -28

• 3b - 7 < 28 and 3b - 7 > -28

• 3b - 7 > 28 and 3b - 7 < -28

What is the interval notation for the solution of |3b - 7| > 28?

• (-∞, -7) ∪ (7, ∞)

• (-∞, -7] ∪ [7, ∞)

• (-7, 7)

• (-7, 7]

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

• Writing the solution in interval notation

• Graphing the solution

• Checking the solution

• Both writing the solution in interval notation and graphing the solution