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Chapter 3: Problem 48

Evaluate each of the following: $$-5-2(-8)$$

Short Answer

Expert verified
-5 - 2(-8) = 11.

Step by step solution

01

- Distribute the Negative Sign

First, multiply \(-2\) by \(-8\). Remember that multiplying two negative numbers results in a positive number. Thus, \(-2 \times -8 = 16\).
02

- Simplify the Expression

Replace the expression \(-2(-8)\) with \(16\), so the entire expression becomes \(-5 + 16\).
03

- Perform the Addition

Finally, add \(-5\) to \(16\). This results in \(16 - 5 = 11\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributing Negative Sign
Understanding how to distribute a negative sign in algebraic expressions is essential. The negative sign outside the parenthesis means that we need to multiply each term inside the parenthesis by that negative number.

In the given problem, we have \(-5 - 2(-8)\). This can be tricky at first, but break it down step by step.

First, focus on the part inside the parenthesis: \(-2 \times -8\). Note that a negative times a negative gives a positive. So, \(-2 \times -8 = 16\). Understanding this helps you see why it becomes a positive number.

After distributing the negative sign, the expression changes to \(-5 + 16\). Next, move forward to simplifying the expression.
Multiplying Negative Numbers
Multiplying negative numbers can sometimes be confusing. Let's break it down.

The rules are quite simple:
  • Negative times a negative equals a positive
  • Negative times a positive equals a negative
  • Positive times a positive equals a positive


Going back to our example: \(-2(-8)\), you multiply the two negative numbers. Knowing the rule, you can now replace it with a positive: \16\.

This transforms the expression to \(-5 + 16\), which is simpler and ready for the final step: addition.
Simplifying Expressions
Simplifying expressions is all about making them as uncomplicated as possible.

After distributing the negative sign and calculating \(-2 \times -8 = 16\), we got the expression \(-5 + 16\). Now, combine these numbers.

Think of \-5\ as taking away 5 from 16. This is straightforward addition and subtraction within an expression.

Finally, \16 - 5 = 11\.

By following the steps鈥攄istributing the negative sign, handling negative multiplication, and simplifying the expression鈥攚e can solve even complex-looking problems with ease. Keep practicing these steps, and you'll get the hang of it!

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