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Chapter 1: Problem 64

Find \(-x\) for each of the following. $$ x=3.14 $$

Short Answer

Expert verified
-3.14

Step by step solution

01

Understand the Problem

We are asked to find the negative of the given value of x. This means we need to multiply the given value by -1.
02

Substitute the Given Value

Given that \( x = 3.14 \), we will substitute this value into the expression \( -x \).
03

Perform the Calculation

Multiply the value of \( x \) by -1: \[ -x = -1 \times 3.14 \]
04

Simplify the Expression

Complete the multiplication: \[ -x = -3.14 \]

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Key Concepts

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

Multiplication by -1
To find the negative of a number, we multiply it by -1. This changes the sign of the number.
For example:
- Multiplying a positive number by -1 makes it negative.
- Multiplying a negative number by -1 makes it positive.
It's a straightforward but essential concept in algebra. For instance, if we have a value of x = 3.14, multiplying by -1 gives us -3.14.
The calculation is simple:
\(-x = -1 \times 3.14 = -3.14\). This operation is key to many algebraic problems.
Substituting Values
Substituting values means replacing variables with their given values in an expression or equation.
First, identify where to insert the given value.
For our example, x = 3.14. We replace x in the expression \-x \ with 3.14.
This step is crucial before performing any calculations.
It changes the abstract expression into something concrete: \(-x = -1 \times 3.14\). Remember to always double-check that you are substituting correctly to avoid mistakes.
Simplifying Expressions
Simplifying expressions makes them easier to understand and work with.
After substituting values and performing operations, simplify to get the final form.
For example, after substitution and multiplication: \(-x = -1 \times 3.14\)
Simplify this to: \[-x = -3.14\]
Simplification might involve combining like terms, reducing fractions, or performing basic arithmetic operations.
Always make sure your final expression is as simple as possible for clarity and correctness.

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