https://file.aiquickdraw.com/mathbot/file/1726875163733arjygtf9.jpg

The equation in the image is:

\[
2 + \frac{4}{3}x = x - \frac{1}{3}
\]

Let's solve this step by step:

### Step 1: Combine like terms
First, move all terms involving \(x\) to one side and constants to the other.

Subtract \(x\) from both sides:
\[
2 + \frac{4}{3}x - x = - \frac{1}{3}
\]

### Step 2: Simplify the \(x\)-terms
\[
\frac{4}{3}x - x = \frac{4}{3}x - \frac{3}{3}x = -\frac{1}{3}
\]

So, the equation becomes:
\[
2 + \frac{1}{3}x = -\frac{1}{3}
\]

### Step 3: Move constants to one side
Subtract 2 from both sides:
\[
\frac{1}{3}x = -\frac{1}{3} - 2
\]

Convert \(2\) to a fraction:
\[
\frac{1}{3}x = -\frac{1}{3} - \frac{6}{3} = -\frac{7}{3}
\]

### Step 4: Solve for \(x\)
Multiply both sides by 3 to get rid of the fraction:
\[
x = -7
\]

### Final Answer:
The solution is \(x = -7\).

Would you like further details or explanations?

Here are some related questions:
1. How do you solve linear equations with fractions?
2. What are the common methods to eliminate fractions in equations?
3. How can you verify solutions for equations with variables?
4. What is the importance of like terms in solving equations?
5. How do we handle equations with both constants and variables?

**Tip**: Always simplify fractions and terms step by step to avoid mistakes.

Solve the equation: 2 + (4/3)x = x - 1/3.

Learn how to solve the linear equation with fractions: 2 + (4/3)x = x - 1/3. This detailed step-by-step solution covers essential algebraic concepts such as combining like terms and solving for x. Suitable for students in Grades 8-10.

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