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Chapter 1: Problem 247

Simplify each expression. $$ -(6-8)-(2-4) $$

Short Answer

Expert verified
The simplified expression is 4.

Step by step solution

01

Simplify inside the parentheses

First, simplify the expressions inside both sets of parentheses. For the first set, calculate \(6-8\), which equals \(-2\). For the second set, calculate \(2-4\), which equals \(-2\).
02

Replace parentheses with simplified values

Replace the expressions inside the parentheses with the simplified values from Step 1. The expression now becomes \(-( -2) - (-2)\).
03

Apply the negative sign

Apply the negative sign outside each set of parentheses. Remember that \(-( -2)\) is equal to \(2\). The expression is now \(2 - (-2)\).
04

Simplify the resulting expression

Simplify the final expression by subtracting a negative number, which is the same as adding the positive. So, \(2 - (-2)\) is equivalent to \(2 + 2\). The final simplified result is \(4\).

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Key Concepts

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

Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and operations. They can involve addition, subtraction, multiplication, and division. In this exercise, the expression involves subtraction of two groups. Understanding how these expressions work is crucial in solving problems correctly. The goal is to find a simpler form that鈥檚 easier to handle.
Negative Numbers
Negative numbers are less than zero and have a minus sign in front of them. They are essential in algebra, especially when dealing with subtraction and addition. For example, in our exercise, we have \(-2\) and \(-2\) inside the parentheses. It鈥檚 important to know that subtracting a negative number is the same as adding a positive number. So, \(-( -2)\) becomes \(+2\).
Parentheses in Algebra
Parentheses are used to group parts of an expression that should be simplified first. This process is known as the order of operations, or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our example, you first simplify inside the parentheses to find the values \(-2\) and \(-2\). Then you handle the expressions outside the parentheses next.
Simplification Steps
Simplifying an expression means breaking it down into its simplest form. Here鈥檚 a summary of the key steps followed in our problem:

  • Simplify inside the parentheses: Calculate the expressions inside each set of parentheses.
  • Replace parentheses with simplified values: Substitute the simplified numbers back into the expression.
  • Apply the negative signs: Consider the sign in front of each number and handle them correctly.
  • Simplify the resulting expression: Combine like terms to reach the final answer.
By following these steps, you ensure each part of the expression is correctly handled, leading to a precise and simplified result.

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