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Chapter 1: Problem 18

Simplify each expression. See Example 1. $$ -(-t) $$

Short Answer

Expert verified
The expression simplifies to \(t\).

Step by step solution

01

Understand the Expression

The expression given is \(-(-t)\). It includes a double negative, which indicates the negative of a negative.
02

Apply the Double Negative Rule

In mathematics, the negative of a negative returns the positive form of the number. Therefore, \(-(-t)\) simplifies to \(t\).

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Key Concepts

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

Simplifying Expressions
When we talk about simplifying expressions, it means making them easier to understand and work with by reducing them to their simplest form. In algebra, this often involves a couple of key steps:
  • Combining like terms, which means adding or subtracting coefficients of similar variables.
  • Applying basic arithmetic operations to reduce the expression as much as possible.
Simplifying expressions helps to solve them easier or to rewrite them in a form that may provide insights about the relationships between variables. For example, in simplifying \(-(-t)\), understanding the fundamentals of working with negative numbers and the effects of double negatives was crucial.
Negative Numbers
Negative numbers are numbers less than zero, and they have some special properties and rules for how they interact with other numbers. Negative numbers represent the opposite or the additive inverse of their positive counterparts. For example, the negative number \(-5\) is the additive inverse of \(5\), meaning when they are combined (added), they result in zero.
  • Adding a negative number is the same as subtracting the absolute value of that number.
  • Multiplying or dividing two negative numbers results in a positive number because the negatives cancel each other out.
  • When subtracting a negative number, it becomes an addition operation.
Understanding these properties is vital when simplifying expressions with negative numbers. Knowing how they interact allows us to handle expressions like \(-(-t)\) correctly.
Double Negative Rule
The double negative rule is a fundamental concept in both mathematics and language. In mathematics, it specifically refers to the property that negating a negative value returns it to its positive state. This is a simplified logical notation that states:
\(-(-t) = t\)
This rule is grounded in the basic understanding that two negative elements generally cancel each other. It's similar to turning around twice, which makes you face the original direction. Here's how it works with numbers:
  • The negative of a negative integer, like \(-(-3)\), becomes \(3\).
  • Applying double negatives can simplify equations, making calculations straightforward and less error-prone.
So, when encountering double negatives in algebraic expressions, remember that you are essentially removing all the negatives, often turning the expression positive.

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Most popular questions from this chapter

Simplify each expression, if possible. $$ t-t-t-t $$

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