Let's solve the inequality $3x + 5 \geq x + 4$.

Step-by-step solution:

1. Move all the terms with $x$ to one side: Subtract $x$ from both sides: $3x - x + 5 \geq 4$ This simplifies to: $2x + 5 \geq 4$

2. Move the constant term to the other side: Subtract 5 from both sides: $2x \geq 4 - 5$ Simplifies to: $2x \geq -1$

3. Solve for $x$: Divide both sides by 2: $x \geq \frac{-1}{2}$ Simplifying: $x \geq -\frac{1}{2}$

Final solution:

$x \geq -\frac{1}{2}$

This means any $x$ greater than or equal to $-\frac{1}{2}$ satisfies the inequality.

Would you like further details or explanations?

Here are 5 related questions:

1. How do you solve compound inequalities?
2. What happens if you multiply or divide by a negative number in inequalities?
3. Can you graph the solution of $x \geq -\frac{1}{2}$ on a number line?
4. How are inequalities different from equations in terms of solution sets?
5. What is the difference between strict inequalities and non-strict inequalities?

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