Exploring Absolute Value Equations and Inequalities

This video tutorial covers absolute value equations and inequalities, explaining their properties and how to solve them. It includes examples of solving equations and inequalities, graphing solutions, and checking for extraneous solutions. The concept of tolerance in manufacturing is also discussed, using absolute value inequalities to describe acceptable measurement ranges.

What is the result of an absolute value operation?

• A fraction

• A complex number

• A non-negative number

• A negative number

What is the absolute value of -4?

• -4

• 8

• 4

• 0

When solving the equation |2x - 1| = 5, what are the possible values of x?

• x = 3 or x = -2

• x = 5 or x = -4

• x = 2 or x = -3

• x = 4 or x = -1

How do you check if a solution to an absolute value equation is valid?

• By graphing the solution

• By substituting the solution back into the original equation

• By solving a different equation

• By using a calculator

What is an extraneous solution?

• A solution that is not derived from the original equation

• A solution that is derived from the original equation but is not valid

• A solution that is always invalid

• A solution that is always valid

In the equation |3x + 2| = 4x + 5, what is the valid solution?

• x = -3

• x = -1

• x = 1

• x = 3

What does the inequality |x| < 5 mean?

• x is not related to zero

• x is exactly 5 units away from zero

• x is less than 5 units away from zero

• x is more than 5 units away from zero

How do you rewrite the inequality |x| < 5 without absolute value symbols?

• x > -5 and x < 5

• -5 > x > 5

• -5 < x < 5

• x < -5 or x > 5

What does the term 'tolerance' refer to in manufacturing?

• The standard deviation of measurements

• The difference between the maximum and minimum accepted values

• The exact measurement of an item

• The average measurement of an item

If the desired height of a race car is 52 inches with a tolerance of 1 inch, what is the absolute value inequality that describes this?

• |H - 52| ≤ 1

• |H + 52| ≤ 1

• |H - 52| ≥ 1

• |H + 52| ≥ 1