How to Solve Word Problems of Absolute Value and Integers?

A word problem is a kind of exercise that contains some details in the form of text as opposed to mathematical notation.

A step-by-step guide to solving word problems of Absolute Value and Integers

Solving word problems that involve absolute values and integers can be a bit tricky, but it can be done by following these steps:

1. Read the problem carefully and identify the variables and the information that is given.
2. Translate the problem into an equation or inequality that involves absolute values.
3. Solve the equation or inequality.
4. Interpret the solution in the context of the problem and check that the answer makes sense.
5. Test your solution with different values to make sure it works.

Some common absolute value and integer problems include finding the distance between two numbers, finding the magnitude of a difference, or finding the value of an absolute expression in terms of integers.

Remember to always keep the definition of absolute value in mind and to think carefully about the meaning of the problem in order to choose the correct approach to solving it.

Word Problems of Absolute Value and Integers – Example 1

Susan measures the temperature of different liquids. The temperature of liquid \(1\) is \(-2\) and liquid \(2\) is \(6\). Which liquid’s temperature is closest to zero?
Solution:
The temperature of liquid \(1\) is \(-2\). The distance between \(0\) and \(2\) is \(2\).
The temperature of liquid \(2\) is \(6\). The distance between \(0\) and \(6\) is \(6\).
So, liquid \(1\) is closest to zero.

Word Problems of Absolute Value and Integers – Example 2

A scientist studies animal behavior. Hawk usually elevates \(44\) feet above sea level, and dolphins elevate \(-27\) feet below sea level. Which animal is farthest from sea level?
Solution:
The elevation of the hawk is \(44\). The distance between \(0\) and \(44\) is \(44\).
The elevation of the hawk is \(-27\). The distance between \(0\) and \(-27\) is \(27\).
So, the hawk is farthest from sea level.