To solve the equation \( \frac{2}{3}x - 4 = x + 1 \), we can follow these steps:

1. **Isolate the variable terms on one side:**

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

2. **Combine like terms:**

   \[
   \frac{2}{3}x - \frac{3}{3}x = 5
   \]

   \[
   -\frac{1}{3}x = 5
   \]

3. **Solve for \( x \):**

   \[
   x = 5 \times -3
   \]

   \[
   x = -15
   \]

So, the solution to the equation is \( x = -15 \).

Would you like more details or have any questions about this solution? Here are some related questions for further practice:

1. Solve \( \frac{3}{4}x - 2 = x + 5 \).
2. Solve \( 2x + 3 = \frac{1}{2}x + 7 \).
3. Solve \( x - \frac{1}{2} = \frac{3}{4}x + 1 \).
4. Solve \( 4x - 1 = 3 + 2x \).
5. Solve \( 5x + 2 = 7x - 6 \).
6. Solve \( \frac{1}{2}x + 4 = 2x - 3 \).
7. Solve \( 3x - 5 = 2x + 7 \).
8. Solve \( x + 2 = \frac{5}{3}x - 1 \).

**Tip:** Always combine like terms and isolate the variable on one side to simplify the equation-solving process.

Learn how to solve the equation 2/3x - 4 = x + 1 with a detailed step-by-step solution. This problem involves isolating the variable terms and combining like terms to simplify the equation. Suitable for students in Grades 7-9.

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