An algebra tile diagram. The left side has 3 tiles each labeled "n" and two tiles each labeled "negative 1". The middle has an equal sign. The right side has 4 tiles each labeled "1".

The algebra tile diagram you've described can be represented by the equation:

\[
3n - 2 = 4
\]

### Explanation:

1. **Left Side**:
   - You have 3 tiles labeled "n", which represents \(3n\).
   - You have 2 tiles labeled "-1", which represents \(-2\).
   - So, the left side of the equation is \(3n - 2\).

2. **Equal Sign**:
   - The equal sign separates the two sides of the equation.

3. **Right Side**:
   - You have 4 tiles each labeled "1", which represents \(4\).
   - So, the right side of the equation is \(4\).

The algebraic equation \(3n - 2 = 4\) is a linear equation. 

### Solving the Equation:

To solve for \(n\):

1. **Add 2 to both sides** to get rid of the \(-2\) on the left:
   \[
   3n - 2 + 2 = 4 + 2
   \]
   \[
   3n = 6
   \]

2. **Divide both sides by 3** to solve for \(n\):
   \[
   \frac{3n}{3} = \frac{6}{3}
   \]
   \[
   n = 2
   \]

### Final Answer:
\(n = 2\).

Would you like a more detailed explanation or have any questions?

### Follow-up Questions:

1. What happens if the right side has a different number of tiles?
2. How would the equation change if there were 4 "n" tiles on the left side?
3. What if the tiles labeled "-1" were replaced with "1" tiles?
4. Can you solve a similar equation with a different number of tiles?
5. What does it mean if the equation has no solution?

### Tip:
When solving linear equations, always aim to isolate the variable on one side to find its value efficiently.

Learn how to solve the linear equation 3n - 2 = 4 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and their solutions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation