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Chapter 1: Problem 15

Simplify each expression. See Example 1. $$ -(-55) $$

Short Answer

Expert verified
The expression -(-55) simplifies to 55.

Step by step solution

01

Understand the Negative Sign

When you see a negative sign in front of a number, it changes the number's sign. If the number is positive, it becomes negative, and if it's negative, it becomes positive.
02

Identify Double Negatives

In the expression \(-(-55)\), there are two negative signs. One negative sign is outside the parentheses, and one is inside. The double negative indicates that the number will be turned positive.
03

Simplify the Double Negative

Use the rule that two negative signs cancel each other out. Therefore, \(-(-55)\) simplifies to \(55\), as the two negatives negate each other making the expression positive.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are the numbers less than zero. They can be easily found on the number line to the left of zero. These numbers are important for numerous real-life applications, such as measuring temperature below zero or calculating a decrease in profit. When dealing with algebraic expressions, it's important to understand how negative numbers interact with other numbers.
  • A negative sign before a positive number makes it negative. For example, \(-5\) simply indicates that \(5\) is less than zero.
  • If a negative sign is placed before a negative number, the number becomes positive.
Understanding these basic principles will ensure you handle negative numbers correctly in algebraic calculations.
Identifying and Handling Double Negatives
Double negatives in mathematics generally lead to simplification in expression. In simple terms, using two negative signs consecutively transforms the number to its opposite sign, effectively making it positive.
  • The expression \( -(-x) \) implies turning the negative of a negative number to positive.
  • For instance, \(-(-5)\) becomes \(5\).
  • The principle is straightforward: two negatives make a positive.
Knowing about double negatives can greatly simplify your work with expressions, especially when combined with other elements like variables and coefficients.
Breaking Down Simplification Steps
Simplifying an algebraic expression is all about reducing it to its simplest form. This means we are combining like terms and eliminating unnecessary signs.
  • Start by evaluating parentheses and brackets first. They usually signify a group of numbers or operations that need to be handled as a single unit.
  • After resolving operations within parentheses, keep an eye out for any double negatives which should be simplified by changing them to a positive.
  • Be systematic: go from one step to another methodically without skipping any parts.
For our specific expression \(-(-55)\):
  • Recognize the double negatives around \(55\).
  • Apply the rule of double negatives, resulting in \(55\).
By following these steps, expressions become clearer and more manageable.

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