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Chapter 2: Problem 41

Solve equation, and check your solution. \(-2.1 m=25.62\)

Short Answer

Expert verified
The solution is \( m = -12.2 \)

Step by step solution

01

Identify the equation

The given equation is \( -2.1m = 25.62 \). We need to solve for the variable \( m \).
02

Isolate the variable

To isolate \( m \), divide both sides of the equation by \( -2.1 \): \[ m = \frac{25.62}{-2.1} \].
03

Perform the division

Calculate the division: \[ m = \frac{25.62}{-2.1} = -12.2 \].
04

Check the solution

Substitute \( m = -12.2 \) back into the original equation to verify: \[ -2.1 \times -12.2 = 25.62 \]. \[ 25.62 = 25.62 \]. Since both sides are equal, the solution is correct.

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Key Concepts

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

Isolating the Variable
To solve any linear equation, the first goal is to isolate the variable. This means getting the variable, like 'm' in our example, all by itself on one side of the equation.
In the exercise, the equation given is \(-2.1m = 25.62\). To isolate 'm', we need to remove the \-2.1\ attached to it.
To do this, we divide both sides of the equation by \-2.1\. This is because the opposite of multiplying by a number is dividing by that number.
So, we write: \[ m = \frac{25.62}{-2.1} \].
By performing this division, we have isolated the variable 'm'.
Performing Division
Now that we have isolated the variable, we need to perform the actual division to find its value. Our equation now looks like this:
\[ m = \frac{25.62}{-2.1} \].
When we divide 25.62 by -2.1, we get \(-12.2\).
So, \[ m = -12.2 \].
Performing the division accurately is crucial in solving linear equations, as it determines the correct value of the variable.
Checking Solutions
After finding the value of the variable, it is important to check if the solution is correct by substituting it back into the original equation.
In this case, we substitute \ m = -12.2 \ back into the original equation \(-2.1m = 25.62\):
\[ -2.1 \times -12.2 = 25.62 \].
Simplifying, we get \ 25.62 = 25.62 \. Since both sides are equal, our solution is correct.
Checking the solution confirms that no mistakes were made during the calculation process, ensuring the final answer is accurate.

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