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

What does the inequality |x - a| ≤ b represent?

Back

It represents all values of x that are within a distance b from a, meaning x is between a - b and a + b.

Front

How do you interpret the absolute value equation |x - 50| < 15?

Back

This means that x is within 15 units of 50, so the solution is 35 < x < 65.

Front

What is the solution to the inequality |x + 3| > 8?

Back

The solution is x > 5 or x < -11.

Front

How can you express a tolerance of 0.5 feet for a street width of 25 feet using absolute value?

Back

The expression is |W - 25| ≤ 0.5.

Front

What does the equation |v - 20| ≤ 0.03 represent in the context of a sports drink bottle?

Back

It indicates that the volume v of the drink is within 0.03 ounces of 20 ounces.

Front

If a salary must be $3000 with a tolerance of $500, how is this expressed using absolute value?

Back

This is expressed as |m - 3000| ≤ 500.

Front

What is the meaning of the inequality |x - 50| < 15 in a real-world context?

Back

It means that the actual amount of money you have is between $35 and $65.

Front

How do you solve the equation |x - 4| = 3?

Back

The solutions are x = 7 and x = 1.

Front

What is the graphical representation of the inequality |x - 2| ≤ 4?

Back

It represents the interval [-2, 6] on a number line.