Absolute Value Word Problems

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you express a tolerance range using absolute value?

Back

A tolerance range can be expressed using the inequality |x - a| ≤ b, where 'a' is the target value and 'b' is the tolerance.

Front

What does the inequality |x - 6| ≤ 0.1 represent?

Back

It represents that the value of x is within 0.1 units of 6, meaning x can range from 5.9 to 6.1.

Front

How do you determine if a circle is open or closed when graphing inequalities?

Back

Use an open circle for < or > (not including the endpoint) and a closed circle for ≤ or ≥ (including the endpoint).

Front

What is the absolute value equation for a price that varies from an average of $750 by $250?

Back

The equation is |x - 750| = 250.

Front

How do you model a situation where you have an unknown amount of money with a known range?

Back

You can model it with the equation |x - 50| = 15, where x is the unknown amount.

Front

What is the absolute value equation for a volume of liquid that must be within 0.03 ounces of 20 ounces?

Back

The equation is |v - 20| = 0.03.

Front

What does the inequality b < 6 indicate about the value of b?

Back

It indicates that b can take any value less than 6.

Front

How do you solve an absolute value equation like |x - a| = b?

Back

You can split it into two cases: x - a = b and x - a = -b, then solve for x.

Front

What is the significance of the absolute value in real-world applications?

Back

Absolute value is used to express distances, tolerances, and deviations in various real-world contexts.