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Chapter 8: Problem 42

Solve. $$ 1.95 \cdot w=0.078 $$

Short Answer

Expert verified
w = 0.04

Step by step solution

01

Understand the Equation

You need to solve for the variable \( w \) in the equation \( 1.95 \times w = 0.078 \).
02

Isolate the Variable

To find \( w \), you need to isolate it on one side of the equation. You can do this by dividing both sides of the equation by 1.95.
03

Perform the Division

Divide 0.078 by 1.95 to isolate \( w \): \[ w = \frac{0.078}{1.95} \]
04

Simplify the Division

Calculate the division to get the value of \( w \): \[ w = 0.04 \]

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Key Concepts

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

Isolating Variables
When solving linear equations, one of the main goals is to isolate the variable. This process involves manipulating the equation so that the variable is by itself on one side.
For example, consider the equation \[ 1.95 \times w = 0.078 \].
Here, our goal is to isolate \( w \). To do this, we need to get rid of the coefficient next to \( w \) (which is 1.95). This often requires using arithmetic operations like addition, subtraction, multiplication, or division.
Arithmetic Operations
Arithmetic operations are the basic building blocks for solving equations. These include addition, subtraction, multiplication, and division.
In the equation \[ 1.95 \times w = 0.078 \], we need to perform division to isolate the variable.
This is based on the principle of inverse operations: multiplication can be undone by division, and vice versa. By dividing both sides of the equation by 1.95, we effectively cancel out the coefficient next to \( w \). This step is crucial because it simplifies the equation and brings us closer to finding the value of the variable.
Division in Equations
Division is a key operation used to isolate variables, especially when they are multiplied by a coefficient.
In the equation \[ 1.95 \times w = 0.078 \], we divide both sides by 1.95 to isolate \( w \).
This gives us: \[ w = \frac{0.078}{1.95} \].
This division step reduces the equation to \( w = 0.04 \).
It is always important to perform the same operation on both sides of an equation to maintain equality. By doing so, we ensure that the solution is accurate and correctly represents the relationship described by the original equation.

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