Solving Absolute Value Inequalities

The video tutorial explains how to write and solve an inequality to determine acceptable diameters for a machine part, which must be 15 cm plus or minus 0.2 cm. It covers the use of absolute value in inequalities, demonstrating how to solve the inequality to find the range of acceptable diameters. The tutorial emphasizes understanding the method for solving absolute value inequalities and provides a step-by-step solution, concluding with a recap of key points.

What is the acceptable diameter range for the machine part?

• 14.5 cm to 15.5 cm

• 15.0 cm to 15.5 cm

• 14.0 cm to 16.0 cm

• 14.8 cm to 15.2 cm

What mathematical concept is used to handle the plus or minus tolerance in the diameter?

• Exponential

• Logarithm

• Square root

• Absolute value

If the diameter is 14.9 cm, what is the result of 14.9 minus 15?

• -0.1

• 1.0

• 0.1

• -1.0

What does the absolute value of a negative number become?

• It remains negative

• It becomes zero

• It becomes a fraction

• It becomes positive

What is the inequality expression for the machine part's diameter?

• |M + 15| ≤ 0.2

• |M - 15| ≥ 0.2

• |M - 15| ≤ 0.2

• |M + 15| ≥ 0.2

What is the result of adding 15 to both sides of the inequality -0.2 ≤ M - 15 ≤ 0.2?

• 14.8 ≤ M ≤ 15.2

• 15.2 ≤ M ≤ 14.8

• 14.0 ≤ M ≤ 16.0

• 15.0 ≤ M ≤ 15.5

What is the range of acceptable diameters for the machine part?

• 14.0 cm to 16.0 cm

• 14.8 cm to 15.2 cm

• 15.0 cm to 15.5 cm

• 14.5 cm to 15.5 cm

What type of statement is used if the inequality is less than?

• And statement

• Or statement

• If statement

• Not statement

What type of statement is used if the inequality is greater than?

• Or statement

• And statement

• Not statement

• If statement

What should you do to ensure you understand the method for solving absolute value inequalities?

• Ignore the problem set

• Memorize the formulas

• Do the problem set

• Skip the lesson