Problem 92 - Intermediate Algebra

Question

In the following exercises, simplify each expression. $$ -(4-5)-(7-8) $$

Step-by-Step Solution

Answer

0

Step 1: Simplify Inside Parentheses

First, simplify the expressions inside the parentheses. (4-5) = -1 (7-8) = -1

Step 2: Apply the Negative Sign

Next, apply the negative sign to the results from step 1. -(-1) = 1 -(-1) = 1

Step 3: Simplify the Final Expression

Subtract the two results from step 2. 1 - 1 = 0

Key Concepts

Order of Operations

When simplifying algebraic expressions, it's crucial to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Using the order of operations ensures that you simplify correctly.

In the given exercise, we followed these steps:

• First, we handled the parentheses, simplifying \(4-5\) and \(7-8\) to get -1 and -1 respectively.
• Then, we dealt with the negative signs outside the parentheses.
• Finally, we subtracted the two simplified results.

This method prevents mistakes and makes sure your answers are accurate.

Negative Numbers

Understanding how negative numbers work is key to simplifying expressions correctly.

Here are some important points about negative numbers:

• Adding a negative number is the same as subtracting a positive one. For instance, \(5 + (-3) = 5 - 3 = 2\).
• Multiplying two negative numbers gives a positive result, for example, \( (-2) \times (-3) = 6\).
• Subtracting a negative number is like adding the opposite. In our problem, we had -(-1), which equaled 1.

These rules and properties help manage negative numbers effectively in expressions.

Parentheses

Parentheses play a crucial role in determining the order in which operations are performed. Always simplify the expressions inside the parentheses first before dealing with other operations.

Here is the step-by-step importance of handling parentheses:

• In \(4-5\), the parentheses tell us to perform the subtraction resulting in -1.
• Next, in \(7-8\), the subtraction inside parentheses results in -1.
• Keeping these results in mind, we then apply any remaining operations outside the parentheses.

Proper use of parentheses helps maintain clarity and ensures that expressions are simplified systematically and accurately.