To solve the inequality \(2x + 4 \geq 5x - 5\), follow these steps:

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

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

### Step 3: Solve for \(x\).
Divide both sides by 3:
\[
\frac{9}{3} \geq x
\]
\[
3 \geq x
\]

### Final answer:
\[
x \leq 3
\]

Thus, the solution is \(x \leq 3\).

Would you like more details or explanations on any step?

Here are 5 related questions for practice:
1. Solve \(4x - 7 \leq 3x + 5\).
2. Solve \(6x + 2 > 8x - 4\).
3. Solve \(3x + 5 \leq 2x + 8\).
4. Solve and graph \(5x - 3 \geq 7x + 4\).
5. Solve \(2(x + 3) \geq 4x - 6\).

**Tip:** When solving inequalities, remember that if you multiply or divide both sides by a negative number, you must reverse the inequality sign.

Learn how to solve the linear inequality 2x + 4 >= 5x - 5 with step-by-step instructions. This problem covers fundamental algebraic concepts such as moving terms, solving inequalities, and finding the solution set. Ideal for students in Grades 6-8.

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