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Chapter 3: Problem 171

In the following exercises, simplify each expression. $$-(6-8)-(2-4)$$

Short Answer

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Step by step solution

01

Identify the Innermost Parentheses

First, focus on the operations inside the parentheses. The expression is oindent \(-(6-8)-(2-4)\). Determine the values inside each set of parentheses.
02

Simplify Inside the Parentheses

Calculate the expressions within the parentheses: oindent \(6-8 = -2\) oindent \(2-4 = -2\). This simplifies our expression to oindent \(-(-2)-(-2)\).
03

Remove the Negative Signs

Recognize that subtracting a negative number is the same as adding a positive number. This means that oindent \(-(-2) = +2\) oindent (the same applies to the second parentheses). So, the expression simplifies further to oindent \(2 + 2\).
04

Add the Remaining Values

Finally, add the simplified values to get oindent \(2 + 2 = 4\).

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Key Concepts

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

Innermost Parentheses
When simplifying an expression with parentheses, it's important to start with the innermost ones. Parentheses indicate which operations should be performed first. For instance, in the given expression \(-(6-8)-(2-4)\), we need to resolve the operations within each set of parentheses before dealing with anything outside them. This involves focusing on the calculations inside \( (6-8) \) and \( (2-4) \) first. By breaking down these components step-by-step, complex expressions become manageable. This method ensures you simplify the problem correctly, avoiding mistakes. Start from the inside and work your way out!
Subtracting Negative Numbers
Subtracting negative numbers might seem tricky, but it's quite straightforward once you understand the rule. When you subtract a negative number, it is the same as adding its positive counterpart. For example:
If we have \(-(-2)\), it becomes \(+2\).
This is an essential concept and helps turn confusing expressions into simpler ones. In our main example, after calculating the inner parentheses, we had \(-( -2 )-( -2)\). Using the rule of subtracting negative numbers, this becomes \( +2 + 2 \). Remember this: subtracting a negative equals adding a positive!
Evaluating Expressions
Once all the parentheses are resolved and negative signs taken care of, the final step is to evaluate the resulting expression. This involves completing the basic arithmetic operations, like addition or multiplication. In our example, after simplifying the inner parentheses and dealing with negative signs, we ended up with \( +2 + 2 \). Now, you just need to add these values together. Finally, we get \( 2 + 2 = 4 \). Always follow the order of operations and simplify step-by-step to ensure accuracy. By breaking down each part and then combining them, you turn seemingly complex expressions into simple math problems.

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