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Chapter 2: Problem 24

Solve equation, and check your solution. \(3 m=10\)

Short Answer

Expert verified
The solution is \( m = \frac{10}{3} \).

Step by step solution

01

- Isolate the Variable

To isolate the variable, divide both sides of the equation by 3. This will give you:\[ m = \frac{10}{3} \]
02

- Simplify the Equation

Simplify the fraction:\[ m = \frac{10}{3} \] which can also be written as approximately 3.33.
03

- Check the Solution

Substitute the value of \(m\) back into the original equation to verify the solution:\[ 3 \times \frac{10}{3} = 10 \]Since both sides of the equation are equal, \(m = \frac{10}{3}\) is a correct solution.

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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 first steps is to isolate the variable. This means you want to get the variable by itself on one side of the equation. For the given problem, the equation is \(3m = 10\).

To isolate \(m\), we need to undo the multiplication of 3 with \(m\). We do this by dividing both sides of the equation by 3.

This gives us:
\[ m = \frac{10}{3} \]
Now, \(m\) is by itself on one side of the equation, meaning we have successfully isolated the variable. This step is crucial because it simplifies the equation and makes it easier to find the value of the variable.
Simplifying Fractions
After isolating the variable, the next step is to simplify the fraction if possible. Simplifying a fraction involves reducing it to its simplest form. However, in this problem, \[ m = \frac{10}{3} \] cannot be simplified further because 10 and 3 have no common factors other than 1.

While the fraction is already in its simplest form, it can also be expressed as a decimal for easier understanding. \[ m \approx 3.33 \]
This step is vital because it ensures the answer is in the most understandable and usable form for further calculations or interpretations.

It's always good to check if fractions can be simplified, as this makes the solution cleaner and often more comprehensible.
Verifying Solutions
After solving the equation and simplifying it, the last important step is to verify the solution. This means checking if the value we found for \(m\) satisfies the original equation. For our problem, we got:
\[ m = \frac{10}{3} \]
To verify, substitute \(m\) back into the original equation \(3m = 10\):
\[ 3 \times \frac{10}{3} = 10 \]
Since both sides of the equation are equal (10 = 10), our solution is verified as correct.

Verification is crucial because it confirms that the solution is accurate. It ensures no mistakes were made during the solving process, giving you confidence in your final answer.

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Most popular questions from this chapter

Write the answer to each problem in terms of the variable. See Example 11. A baseball player got 65 hits one season. He got \(h\) of the hits in one game. What expression represents the number of hits he got in the rest of the games?

Convert each decimal to a percent. $$ 0.125 $$

Write the answer to each problem in terms of the variable. See Example 11. A bank teller has \(t\) dollars, all in \(\$ 5\) bills. What expression represents the number of \(\$ 5\) bills the teller has?

Translate each statement into an inequality. Use \(x\) as the variable. Tracy could spend at most \(\$ 20\) on a gift.

Simplify each expression. \(-4(-1+6 x)\)
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