Problem 49 - Introductory Algebra for College Students

Question

Perform the indicated subtraction. $$3 \pi-(-10 \pi)$$

Step-by-Step Solution

Answer

The solution to the problem \(3 \pi-(-10 \pi)\) is \(13 \pi\).

Step 1: Recognise the mathematical rule

Notice that the operation is the subtraction of a negative number, which is equivalent to the addition of a positive number. The mathematical rule here is subtracting a negative equals adding a positive. So, the equation \(3 \pi - (-10 \pi)\) becomes \(3 \pi + 10 \pi\).

Step 2: Perform the addition

Now, simply add the two terms together. Both terms are multiples of \( \pi \), so they can be added together directly. This becomes \(3 \pi + 10 \pi = 13 \pi\).