Problem 122 - Introductory Algebra for College Students

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The difference between 0 and a negative number is always a positive number.

Step-by-Step Solution

Answer

The statement - 'The difference between 0 and a negative number is always a positive number' is true.

Step 1: Analyze the statement

Firstly, the statement needs to be analyzed. It's stated that the difference between 0 and a negative number is always a positive number. The word 'difference' speaks of subtraction.

Step 2: Test the statement with an example

For instance, let's take -3 as the negative number. So the difference between 0 and -3 would be \(0 - (-3) = 0 + 3 = 3\). As seen 3 is a positive number.

Step 3: Formulate the correct statement

According to the example, the given statement 'The difference between 0 and a negative number is always a positive number.' appears to be true, because the difference between 0 and any negative number will always result in a positive number. Subtraction of a negative number is the same as adding the absolute value of that number, hence it will give a positive value.