To solve the equation:

\[
\frac{2x}{3} + 4 = x - 5
\]

### Step 1: Eliminate the fraction
Multiply every term of the equation by 3 to get rid of the denominator:

\[
3 \times \left( \frac{2x}{3} + 4 \right) = 3 \times (x - 5)
\]

This simplifies to:

\[
2x + 12 = 3x - 15
\]

### Step 2: Rearrange the terms
Move all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 2x \) from both sides:

\[
12 = x - 15
\]

### Step 3: Solve for \( x \)
Add 15 to both sides to isolate \( x \):

\[
12 + 15 = x
\]

\[
x = 27
\]

So, the solution is \( x = 27 \).

Would you like more details or have any questions?

Here are some related questions for further practice:
1. Solve \( \frac{3x}{4} + 7 = x - 2 \).
2. Solve \( 5x + 8 = 2x + 20 \).
3. Solve \( \frac{x}{2} - 3 = 5 \).
4. Solve \( 4x + 6 = 2x - 8 \).
5. Solve \( \frac{5x}{6} - 4 = 2x + 1 \).

**Tip:** When dealing with fractions, multiplying through by the denominator is a good way to simplify the equation.

This guide explains how to solve the linear equation 2x/3 + 4 = x - 5 by eliminating the fraction, rearranging terms, and solving for x. Suitable for students in Grades 8-10, it covers key algebraic concepts such as working with fractions and solving linear equations.

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