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.

Learn how to solve the linear inequality 3x + 5 ≥ x + 4 with a clear step-by-step breakdown. This solution covers fundamental algebraic techniques, including transposing terms and dividing inequalities. Ideal for students in Grades 6-8.

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