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Chapter 1: Problem 26

\(-(-3)\)

Short Answer

Expert verified
3

Step by step solution

01

Understand the Problem

The expression \(-(-3)\) involves eliminating the double negative.
02

Apply the Double Negative Rule

Recall that subtracting a negative number is equivalent to adding the positive version of that number. Hence, \(-(-3)\) becomes \(+3\).
03

Simplify the Expression

The expression simplifies to \(+3\). Therefore, \(-(-3) = 3\).

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Key Concepts

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

Double Negative
In algebra, encountering a double negative might seem confusing at first, but it follows a simple rule. When you have two negative signs next to each other, they cancel each other out and turn into a positive sign.

For instance, let's look at the expression \(-(-3)\). Here, you see two negative signs: the first one outside the parentheses and the second one inside the parentheses. According to the double negative rule, these two negatives will cancel each other out.

So, \(-(-3)\) simplifies to \(+3\). This rule helps simplify expressions involving multiple negative signs, making the calculations straightforward.
Simplification
Simplification in algebra means breaking down complex expressions into simpler forms. When dealing with double negatives, understanding the rule helps simplify the problem quickly.

In our exercise, the expression \(-(-3)\) initially appears more complicated than it is. Once we apply the double negative rule, it transforms into \(+3\). Simplifying expressions involves steps such as:
  • Identifying and understanding the operations involved
  • Applying the relevant mathematical rules
  • Writing the simplified result


Following these steps ensures you simplify expressions accurately and efficiently.
Negative Numbers
Negative numbers can make calculations seem tricky, but they follow specific rules that when mastered make algebra easier.

A negative number is simply a number less than zero, represented with a minus sign (-). Working with negative numbers involves understanding how they interact with operations like addition, subtraction, multiplication, and division.

Key rules to remember include:
  • Adding a negative number is the same as subtracting its positive counterpart.
  • Subtracting a negative number is equivalent to adding its positive counterpart (this is where the double negative rule comes in).


For example, in our exercise, \(-(-3)\) means subtracting a negative number, which is the same as adding the positive version of that number, resulting in \(+3\). Familiarity with these rules helps in solving algebraic expressions involving negative numbers efficiently.

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Most popular questions from this chapter

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