Solving Absolute-Value Inequalities Effectively

This video tutorial covers solving absolute value inequalities, focusing on both less than and greater than scenarios. It explains how to interpret and solve these inequalities using compound inequalities, providing a cheat sheet for understanding the concepts. The tutorial includes examples across three levels of difficulty, demonstrating how to isolate absolute values, determine the type of inequality, and graph the solutions. Special cases and the use of decimals are also discussed.

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

• Add a constant to both sides

• Get the absolute value by itself

• Combine like terms

• Multiply both sides by a constant

When dealing with an absolute value inequality that is 'less than', what type of compound inequality do we use?

• And

• Or

• Neither

• Both

If the absolute value of x is greater than 5, which of the following represents the correct inequality?

• x > 5 and x < -5

• x < 5 or x > -5

• x > 5 or x < -5

• x < 5 and x > -5

In a 'greater than' absolute value inequality, what type of compound inequality do we use?

• Or

• Both

• And

• Neither

What is the correct inequality for the absolute value of x being less than 3?

• x > 3 and x < -3

• x < 3 or x > -3

• x > 3 or x < -3

• x < 3 and x > -3

When solving an absolute value inequality with additional operations outside the absolute value, what is the first step?

• Add the constant to both sides

• Divide both sides by a constant

• Subtract the constant from both sides

• Multiply both sides by a constant

In level 2 examples, what do you do after isolating the absolute value?

• Multiply both sides by a constant

• Add a constant to both sides

• Analyze the inequality sign

• Combine like terms

For the inequality |x - 8| + 5 > 11, what is the first step?

• Divide both sides by 5

• Multiply both sides by 5

• Add 5 to both sides

• Subtract 5 from both sides

In level 3 examples, what is different about the values inside the absolute value?

• They are always positive

• They are always the same

• They are always negative

• They can be different values

What is the correct inequality for |x + 3| ≤ 3?

• x + 3 ≥ -3 and x + 3 ≤ 3

• x + 3 ≤ -3 or x + 3 ≥ 3

• x + 3 ≥ -3 or x + 3 ≤ 3

• x + 3 ≤ -3 and x + 3 ≥ 3