Exploring Absolute Value Inequalities

This video tutorial explains how to solve absolute value inequalities, focusing on two types: less than and greater than inequalities. The instructor provides examples and step-by-step solutions for each type, demonstrating how to isolate the variable and solve the inequalities. The video concludes with a summary and offers additional resources for further learning.

What are the two types of absolute value inequalities?

• Positive and negative

• Less than or equal to and greater than or equal to

• Equal to and not equal to

• Less than and greater than

If the absolute value of something is less than a number, what does the solution look like?

• X is in between the negative and positive values of the number

• X is equal to the number

• X is greater than the positive value of the number

• X is less than the negative value of the number

In the inequality |2x - 5| ≤ 7, what is the first step to solve it?

• Divide all sides by 2

• Multiply all sides by 2

• Add 5 to all sides

• Subtract 5 from all sides

After adding 5 to all sides in the inequality |2x - 5| ≤ 7, what is the next step?

• Divide all sides by 2

• Multiply all sides by 2

• Add 7 to all sides

• Subtract 5 from all sides

What is the final solution for the inequality |2x - 5| ≤ 7?

• X is between -1 and 12

• X is between -1 and 6

• X is between -7 and 7

• X is between -2 and 12

If the absolute value of something is greater than a number, what does the solution look like?

• X is greater than the negative value of the number

• X is equal to the number

• X is in between the negative and positive values of the number

• X is less than the negative value of the number or greater than the positive value of the number

In the inequality |−3x + 2| > 7, what is the first step to solve the left inequality?

• Subtract 2 from both sides

• Multiply both sides by -3

• Divide both sides by -3

• Add 2 to both sides

After subtracting 2 from both sides in the inequality |−3x + 2| > 7, what is the next step?

• Multiply both sides by -3

• Add 2 to both sides

• Subtract 7 from both sides

• Divide both sides by -3

What happens to the inequality sign when you divide both sides by a negative number?

• It stays the same

• It flips

• It becomes an equal sign

• It becomes a not equal sign

What is the final solution for the inequality |−3x + 2| > 7?

• X is less than 3 or greater than -5/3

• X is greater than 3 or less than -5/3

• X is equal to 3 or -5/3

• X is between -3 and 5/3