Absolute Value Inequalities Word Problems

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that involves the absolute value of a variable, expressing the distance of that variable from a certain value.

Front

How do you express a range of values using absolute value?

Back

A range of values can be expressed using absolute value as |x - a| ≤ b, where 'a' is the central value and 'b' is the allowable distance from 'a'.

Front

What does the equation |v - 20| = 0.03 represent?

Back

It represents that the volume 'v' of a bottle is within 0.03 ounces of 20 ounces.

Front

What is the solution to the inequality |w - 213| ≤ 5?

Back

The solution is 208 ≤ w ≤ 218, meaning the weight of the box must be between 208 grams and 218 grams.

Front

What does the equation |W - 25| ≤ 0.5 signify in a street width problem?

Back

It signifies that the width 'W' of the street must be within 0.5 feet of 25 feet.

Front

How do you find the maximum and minimum values from an absolute value equation?

Back

To find the maximum and minimum values, solve the equation |x - a| = b to get x = a + b and x = a - b.

Front

What is the meaning of the equation |x - 300| = 25 in the context of temperature?

Back

It means that the temperature 'x' for roasting cocoa beans can vary 25 degrees above or below 300 degrees Fahrenheit.

Front

What does the expression |x - 50| = 15 indicate about the amount of money you have?

Back

It indicates that the amount 'x' you have is 15 dollars more or less than 50 dollars, so it can range from 35 to 65 dollars.

Front

What is the general form of an absolute value inequality?

Back

The general form is |x - a| < b or |x - a| > b, where 'a' is a specific value and 'b' is a distance.

Front

How do you interpret |x - a| < b?

Back

It means that 'x' is within 'b' units of 'a', or a range of values around 'a'.