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Chapter 8: Problem 335

In the following exercises, solve each equation. $$ 9 m-2-4 m+m=42-8 $$

Short Answer

Expert verified
m = 6

Step by step solution

01

Combine Like Terms

Combine the terms involving variable m on the left side: \( 9m - 4m + m \). Simplify this to: \( 6m \)
02

Simplify the Equation

Simplify the equation by combining all the constants: \( 6m - 2 = 34 \)
03

Isolate the Variable

Add 2 to both sides to isolate the term with \( m \): \( 6m = 36 \)
04

Solve for the Variable

Divide both sides by 6 to solve for \( m \): \( m = 6 \)

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Key Concepts

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

Combining Like Terms
When solving linear equations, it's essential to combine like terms first. Like terms are terms that have the same variable raised to the same power.
In the given exercise, you have the terms involving the variable \(m\) on the left side: \(9m - 2 - 4m + m = 42 - 8\).
The like terms here are \(9m\), \(-4m\), and \(m\). Combining these terms helps simplify the equation.
Perform the addition: \(9m - 4m + m\), which yields \(6m\).
Now, the equation looks cleaner and more straightforward: \(6m - 2 = 34\) after handling all constants appropriately.
Simplifying Equations
Once you have combined like terms, the next step is to simplify the equation further. This means getting rid of any constants or unnecessary parts so that the equation is easier to solve.
In this exercise, we recognized that \(6m - 2 = 34\) can be simplified by addressing the constants.
Simplify the right side of the original equation \(42 - 8\), which gives \(34\).
Now, you have an equation: \(6m - 2 = 34\). This step is crucial as it prepares the equation for isolating the variable.
Isolating the Variable
Isolating the variable is a key step to finding its value. You achieve this by performing operations that will leave the variable term on one side of the equation, and constants on the other side.
In this case, the equation is \(6m - 2 = 34\).
To isolate \(m\), add 2 to both sides of the equation to cancel out the \(-2\) on the left side.
This step will result in: \(6m = 36\).
By isolating the variable, you make it straightforward to determine the value of \(m\).
Solving for a Variable
Finally, to solve for the variable, you need to perform the arithmetic that will give you the variable's value.
After isolating the term involving the variable, you'll likely end up with a simpler equation.
In this scenario, you have \(6m = 36\).
To solve for \(m\), divide both sides by 6 鈬� \(m = 6\).
Double-check your solution by substituting \(m = 6\) back into the original equation to ensure it satisfies the equation.
This confirms that your solution is correct and solidifies your understanding of the process.

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