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Chapter 1: Problem 60

Find \(-x\) for each of the following. $$ x=12 $$

Short Answer

Expert verified
-12

Step by step solution

01

Identify the Given Value

The given value of the variable is provided in the problem. Here, it is given that \( x = 12 \).
02

Understand \(-x\)

The question asks to find \(-x\). This means we need to find the negative value of \( x \).
03

Substitute the Given Value

Substitute the given value of \( x \) into the expression \(-x\). Thus, \(-x = -(12)\).
04

Simplify

Simplify the expression. Negating 12 results in \(-12\). Therefore, \(-x = -12\).

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Key Concepts

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

Variables
In mathematics, variables are symbols that stand in for unknown or changing values. In our exercise, the variable is given as \(x = 12\). Here, \(x\) is simply representing the number 12. The use of variables allows us to generalize mathematical concepts and work with equations more flexibly.
Variables help us to:
  • Represent unknowns in equations.
  • Perform algebraic manipulations.
  • Create general formulas.
In more complex problems, the values of variables can change, making it crucial to understand how to work with them properly.
Negation
Negation in mathematics refers to changing the sign of a number. If you start with a positive number, its negation is negative, and vice versa. When the exercise asks for \(-x\), it means we need to find the negative value of \(x\).
For example, if \(x = 12\), then \(-x = -12\). This concept is similar to flipping the value across zero on the number line.
Negation is often signified by a minus sign (\(-\)) preceding the number or variable. So, understanding this means:
  • If \(x = 5\), then \(-x = -5\).
  • If \(x = -7\), then \(-x = 7\).
Negation helps in solving algebraic equations and simplifies many mathematical operations by ensuring a clear understanding of how positive and negative values interact.
Simplification
Simplification is the process of reducing a mathematical expression to its simplest form. For our exercise, this involves substituting the given variable and then performing arithmetic operations.
Initially, we identified the variable \(x\) as 12. To find \(-x\), we substitute \(x\) into the expression \(-x\), giving us \(-x = -(12)\). Simplifying this yields \(-12\).
Simplification steps include:
  • Substituting variables.
  • Performing arithmetic operations.
  • Reducing expressions to cleaner and more understandable forms.
By simplifying expressions, we make equations easier to work with and understand, providing a clear path to the solution.

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Most popular questions from this chapter

Insert one pair of parentheses to convert each of the following false statements into a true statement. $$ 2-7 \cdot 2^{2}+9=-11 $$

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