https://file.aiquickdraw.com/mathbot/file/1729881719690dvxblakg.jpg

The equation provided in the image is:

\[
4n + 3 = 10n + 7
\]

We need to determine which of the given values of \( n \) satisfies this equation. Let's solve it step by step:

1. First, subtract \( 4n \) from both sides of the equation to get the terms involving \( n \) on one side:

\[
3 = 6n + 7
\]

2. Now, subtract 7 from both sides to isolate the term with \( n \):

\[
-4 = 6n
\]

3. Finally, divide both sides by 6:

\[
n = -\frac{4}{6} = -\frac{2}{3}
\]

Thus, the correct solution is:

\[
n = -\frac{2}{3}
\]

This corresponds to option (2).

Do you want any additional details or clarifications?

Here are 5 related questions:
1. How do you verify the solution by plugging the value back into the original equation?
2. Can you explain the importance of isolating the variable in linear equations?
3. What other types of equations could arise from a similar problem?
4. How would the steps differ if fractions appeared earlier in the equation?
5. How do you handle an equation with variables on both sides?

**Tip**: Always check your solution by substituting it back into the original equation to confirm it satisfies all terms.

Which of the following values solves the equation 4n + 3 = 10n + 7?

Learn how to solve the linear equation 4n + 3 = 10n + 7 with a step-by-step solution. This problem involves algebraic concepts such as isolating variables and solving linear equations. Suitable for students in Grades 7-9.

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