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Chapter 2: Problem 32

Solve the given equation for \(\mathrm{x}\). \(\frac{x}{-6}=-20\)

Short Answer

Expert verified
The solution is \(x = 120\).

Step by step solution

01

Identify the Given Equation

The equation given is \(\frac{x}{-6} = -20\). We need to solve for \(x\).
02

Isolate the Variable

To isolate \(x\), multiply both sides of the equation by \(-6\). This will cancel \(-6\) from the denominator on the left side. The equation becomes: \(x = -20 \times (-6)\).
03

Multiply the Numbers

Now, calculate the right side: \(-20 \times (-6)\). When multiplying two negative numbers, the result is positive. Thus, \(-20 \times (-6) = 120\).
04

Write the Solution

The solution to the equation \(\frac{x}{-6} = -20\) is \(x = 120\).

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Key Concepts

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

Prealgebra
Prealgebra is a foundational mathematical level that introduces basic algebra concepts. It's the stepping stone before students advance to algebra. In prealgebra, you'll learn numbers, simple algebraic expressions, and equations.

Understanding prealgebra prepares students for more complex mathematical topics. It teaches you how to manipulate numbers and simple variables without getting bogged down with complicated processes.

Key elements include:
  • Numerical operations such as addition, subtraction, multiplication, and division.
  • Working with whole numbers, fractions, and decimals.
  • Introduction to variables and simple equations.
When solving equations like \(\frac{x}{-6} = -20\) in prealgebra, you apply these basic operations. Here, you have a simple equation where understanding multiplication and division of numbers is vital.
Multiplication of Negative Numbers
When you multiply negative numbers, it鈥檚 important to remember the rules because they might feel a bit tricky.

In mathematics, multiplying:
  • Two positive numbers results in a positive product.
  • Two negative numbers gives you a positive product.
  • A positive number and a negative one results in a negative product.
In our example equation \(x = -20 \times (-6)\), you multiply two negative numbers.

The result is positive, leading us to \(x = 120\).

This principle helps build an understanding of how negative numbers interact in algebra and lays the groundwork for dealing with more complicated equations later on.
Isolation of Variables
Isolation of variables is an essential concept in algebra and prealgebra. In simple terms, it means rearranging an equation so that the variable you want to solve for is all alone on one side of the equation.

For our equation \(\frac{x}{-6} = -20\):
  • First, identify what you need to do to both sides of the equation to get \(x\) by itself.
  • Here, multiplying both sides by \(-6\) isolates \(x\).
  • This action cancels the \(-6\) in the denominator, giving you \(x = -20 \times (-6)\).
This process is foundational in solving equations because it helps you to systematically and logically get the answer.

The concept of isolating variables becomes more crucial as you move on to more complex algebraic equations.

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Most popular questions from this chapter

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