We can solve the inequality step by step:

### Given:
\[
2x + 4 \geq 5x - 5
\]

### Step 1: Move all terms involving \(x\) to one side.
Subtract \(2x\) from both sides:
\[
4 \geq 5x - 2x - 5
\]
\[
4 \geq 3x - 5
\]

### Step 2: Move constants to the other side.
Add 5 to both sides:
\[
4 + 5 \geq 3x
\]
\[
9 \geq 3x
\]

### Step 3: Solve for \(x\).
Divide both sides by 3:
\[
x \leq 3
\]

Thus, the solution is:
\[
x \leq 3
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do you solve inequalities involving fractions?
2. What happens if you multiply or divide by a negative number in inequalities?
3. How can you represent this inequality on a number line?
4. How do you solve quadratic inequalities?
5. How do compound inequalities differ from simple inequalities?

**Tip:** When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number!

Learn how to solve the linear inequality 2x + 4 ≥ 5x - 5 with a clear step-by-step solution. This example covers important algebraic concepts and demonstrates how to manipulate inequalities. Ideal for students in Grades 7-9.

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