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.