Solving Multi-Step Absolute-Value Inequalities

This video tutorial covers solving multi-step absolute value inequalities. It begins with an introduction to the concept and then provides detailed solutions to several example problems, labeled A through F. Each problem is solved step-by-step, demonstrating how to isolate the absolute value expression and solve the resulting inequalities. The tutorial concludes with a word problem involving the weight of a basketball, illustrating how to apply these concepts in a real-world context.

What is the first step in solving a multi-step absolute value inequality?

• Combine like terms

• Isolate the variable

• Distribute any constants

• Isolate the absolute value expression

In the inequality 5|x + 6| < 31, what is the result after subtracting 6 from both sides?

• 5|x + 6| < 25

• 5|x| < 25

• 5|x + 6| < 37

• 5|x| < 31

When solving |x/7 - 3| ≥ 4, what is the next step after adding 3 to both sides?

• Divide both sides by 7

• Multiply both sides by 7

• Subtract 3 from both sides

• Add 7 to both sides

What does the inequality |x - 9| ≤ 7 translate to in terms of 'and' statements?

• x - 9 ≤ 7 and x - 9 ≥ -7

• x - 9 ≥ 7 or x - 9 ≤ -7

• x - 9 ≤ 7 or x - 9 ≥ -7

• x - 9 ≥ 7 and x - 9 ≤ -7

In the inequality -4|x + 9| > -10, what must you remember to do after dividing by -4?

• Keep the inequality sign the same

• Subtract 4 from both sides

• Flip the inequality sign

• Add 4 to both sides

What is the solution to the inequality |x/2 + 5| < 7?

• -9 < x < 9

• -14 < x < 14

• -2 < x < 2

• -4 < x < 4

How do you graph the solution to the inequality |5x - 5| > 10?

• Shade only the right side

• Shade only the left side

• Shade outside the points

• Shade between the points

What is the acceptable weight range for a basketball if it can vary no more than 1 ounce from 21 ounces?

• 21 to 23 ounces

• 19 to 23 ounces

• 20 to 22 ounces

• 20 to 21 ounces

In the word problem, what does the inequality |W - 21| ≤ 1 represent?

• The weight must be less than 21 ounces

• The weight can be 1 ounce more or less than 21 ounces

• The weight must be exactly 21 ounces

• The weight must be more than 21 ounces

What is the final step in solving the word problem involving the basketball's weight?

• Add 21 to all sides

• Subtract 21 from all sides

• Divide all sides by 21

• Multiply all sides by 21