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Chapter 2: Problem 67

Solve each equation, and check the solution. $$ 5 m+6 m-2 m=63 $$

Short Answer

Expert verified
m = 7

Step by step solution

01

Combine like terms

Combine the terms involving the variable m on the left side of the equation: 5m + 6m - 2m. Adding these together yields 9m.
02

Rewrite the equation

The equation now becomes 9m = 63.
03

Solve for m

To isolate m, divide both sides of the equation by 9. \[ m = \frac{63}{9} = 7 \]
04

Check the solution

Substitute m = 7 back into the original equation to verify the solution: \[ 5(7) + 6(7) - 2(7) = 35 + 42 - 14 = 63 \]. Since both sides of the equation match, the solution is correct.

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Key Concepts

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

Combining Like Terms
To start solving a linear equation, the first thing you often do is combine like terms. In the given problem, the equation is: \(5m + 6m - 2m = 63\).
Here, all terms involving the variable \(m\) are on the left side. Combining like terms means adding or subtracting them to simplify the equation.
In this case, you add 5m, 6m, and subtract 2m.
This gives:
\(5m + 6m - 2m = 9m\).
Now, the equation looks a lot simpler: \(9m = 63\).
Combining like terms helps to reduce the complexity and makes it easier to proceed to the next steps.
Isolating Variables
Once the terms are combined, the next step is to isolate the variable you're solving for.
In our simplified equation \(9m = 63\), we need to solve for \(m\). This is done by isolating \(m\) on one side of the equation.
You achieve this by performing operations that will leave \(m\) alone on one side. Here, you divide both sides of the equation by 9:
\[m = \frac{63}{9} = 7\].
With \(m\) isolated, it becomes clear that \(m = 7\). Isolating variables simplifies the equation further and leads us to the solution quickly.
Verifying Solutions
After isolating the variable and finding a solution, the last crucial step is to verify the solution. This makes sure your answer is correct.
You do this by substituting the solution back into the original equation.
For our problem, substitute \(m = 7\) back into the original equation:
\[5(7) + 6(7)-2(7)\]
Simplify each term:
\[35 + 42 - 14\]
Finally, add or subtract the simplified terms:
\[63 = 63\]. Both sides of the equation match, confirming our solution is correct.
Verifying the solution is a necessary step to ensure accuracy and trust in the results.

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Most popular questions from this chapter

Solve each equation for \(y\) $$ x-5 y=10 $$

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