Problem 59 Find $-x$ for each of the foll... [FREE SOLUTION]

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Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 1: Problem 59

Find $-x$ for each of the following. $$ x=8 $$

Short Answer

Expert verified

-8

Step by step solution

Identify the Given Value

The given value for the variable is $x = 8$.

Set Up the Expression for $-x$

We need to find $-x$. This means taking the negative of the given value of $x$.

Calculate $-x$

Plug in the given value into the expression for $-x$: $-x = -8$.

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Key Concepts

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

Variable Negation

In algebra, negating a variable simply means finding its opposite value. For instance, if we have a variable $x$ with a value of $8$, the negation of $x$ is written as $-x$. This means we are switching the sign from positive to negative. So, if $x = 8$, then $-x = -8$. Understanding variable negation is crucial since it is frequently used in various algebraic operations. Remember, negation does not change the magnitude, only the sign.

Basic Algebraic Operations

Algebraic operations, such as addition, subtraction, multiplication, and division, are foundational in solving any mathematical problem. When working with variables, these operations help in simplifying expressions and solving equations.
For example, knowing how to negate a variable is part of these basic operations. Consider the steps:

Identify the variable and its value. In our case, $x = 8$.
Create the expression for the negated variable: $-x$.
Substitute the given value into the expression: $-x = -8$.

This process is straightforward but essential for more complex algebraic manipulations.

Negative Numbers

A negative number is a number that is less than zero. It is represented with a minus sign ($-$). Basic arithmetic rules apply to negative numbers, just as they do for positive numbers. Here are some key points to remember:

Adding two negative numbers results in a more negative number: $-2 + (-3) = -5$.
Subtracting a negative number is like adding a positive number: $-5 - (-3) = -2$.
Multiplying or dividing two negative numbers results in a positive number: $-2 \times -3 = 6$, and $-6 \div -2 = 3$.
Multiplying or dividing a positive number with a negative number yields a negative result: $2 \times -3 = -6$, and $-6 \div 2 = -3$.

In our exercise, when we negate a positive number like $8$, the result is a negative number: $-8$. This switch of signs is integral to understanding how to properly apply and manipulate negative numbers in algebra.

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91影视

Find \(-x\) for each of the following. $$ x=8 $$

Short Answer

Step by step solution

Identify the Given Value

Set Up the Expression for \(-x\)

Calculate \(-x\)

Key Concepts

Variable Negation

Basic Algebraic Operations

Negative Numbers

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