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 solve the inequality |x + 3| > 8?

Back

Split into two cases: x + 3 > 8 or x + 3 < -8. This leads to x > 5 or x < -11.

Front

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

Back

It represents all values of x that are within b units of a on the number line.

Front

How do you express a distance constraint using absolute value?

Back

If a distance must be within a certain range, use |x - a| ≤ d, where a is the center point and d is the distance.

Front

What is the solution set for the inequality |x - 6| ≤ 0.1?

Back

The solution set is 5.9 ≤ x ≤ 6.1.

Front

How do you write an inequality for being within 14 miles of school, give or take 3 miles?

Back

The inequality is |x - 14| ≤ 3, which simplifies to 11 ≤ x ≤ 17.

Front

What is the significance of the tolerance in manufacturing?

Back

Tolerance defines the acceptable range of variation in a manufactured part, ensuring it meets quality standards.

Front

How do you solve the inequality 3 |2x + 7| - 7 < -4?

Back

First, isolate the absolute value: |2x + 7| < 1. Then split into two cases: 2x + 7 < 1 and 2x + 7 > -1.

Front

What is the formula for the maximum and minimum volume of a liquid in a bottle with a target volume of 20 ounces and a tolerance of 0.03 ounces?

Back

The formula is |v - 20| ≤ 0.03, leading to 19.97 ≤ v ≤ 20.03.

Front

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

Back

It represents all values of x that are at least 0.1 units away from 6.