Solving Absolute-Value Inequalities Effectively

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