Understanding Absolute Value Inequalities

The video tutorial explains how to solve an inequality involving the absolute value of y plus 22 being less than or equal to 13.5. The process involves isolating the absolute value on one side and simplifying the inequality. However, it is shown that the absolute value cannot be less than or equal to a negative number, leading to the conclusion that there is no solution to the problem.

What is the initial inequality given in the problem?

• |y - 22| ≤ 13.5

• |y + 22| ≥ 13.5

• |y + 22| > 13.5

• |y + 22| ≤ 13.5

What is the first step to isolate the absolute value of y?

• Subtract 22 from both sides

• Multiply both sides by 22

• Divide both sides by 22

• Add 22 to both sides

Tags

CCSS.7.NS.A.1C

What is the result of 13.5 minus 22?

• -8.5

• 8.5

• -9.5

• 9.5

Why is it impossible for the absolute value of y to be less than or equal to -8.5?

• Absolute values are always positive

• Absolute values can be zero or negative

• Absolute values are always non-negative

• Absolute values can be negative

What conclusion is reached about the solution to the inequality?

• The solution is y = 0

• There is no solution

• There are multiple solutions

• There is a unique solution