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Chapter 2: Problem 91

Solve for \(x .\) Assume \(a, c, m \neq 0\) $$ m x=9.4 m $$

Short Answer

Expert verified
x = 9.4

Step by step solution

01

Understand the problem

You need to isolate the variable 'x' on one side of the equation to solve for it.
02

Identify the given equation

The given equation is ewline \[ m x = 9.4 m \]
03

Divide both sides by the coefficient of x

Divide both sides of the equation by 'm'. Since 'm 鈮� 0', you can safely perform this step: ewline \[ x = \frac{9.4 m}{m} \]
04

Simplify the equation

After dividing, the 'm' terms on the right side cancel each other out, simplifying to: ewline \[ x = 9.4 \]

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Key Concepts

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

Isolation of Variables
In algebra, solving equations often involves isolating the variable you want to solve for. This means getting the variable alone on one side of the equation.
For example, consider the equation: \[ m x = 9.4 m \].
Our goal is to solve for the variable 'x'.
To isolate 'x', you need to move everything else away from it. In this equation, 'm' is multiplied by 'x'.
So, you'll need to perform the opposite operation (in this case, division) to isolate 'x'. This process of isolation helps simplify the problem and makes it easier to solve for the desired variable. By focusing on isolating the variable, you can methodically work towards the solution.
Division in Algebra
Division is a fundamental operation in algebra, especially when isolating variables. It is used to undo multiplication.
For instance, in the equation \[ m x = 9.4 m \], 'x' is multiplied by 'm'.
To isolate 'x', you'll need to divide both sides of the equation by 'm': \[ x = \frac{9.4 m}{m} \].

Remember to treat both sides of the equation equally; whatever operation you perform on one side, you must do to the other side, as well. This maintains the balance of the equation.

Also, make sure
Simplification of Algebraic Expressions
Simplification is the process of reducing an algebraic expression to its simplest form.
This often includes canceling out like terms, simplifying fractions, and performing basic arithmetic operations.
In our example, once you've divided both sides of the equation by 'm', you get: \[ x = \frac{9.4 m}{m} \]. Since 'm' in the numerator and the denominator are the same, they cancel each other out, simplifying to: \[ x = 9.4 \].
This simplification step is crucial as it reduces the equation to a form where the variable 'x' is now clearly isolated and solved for.
Always check your work by substituting the obtained value back into the original equation to verify its correctness.

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