https://file.aiquickdraw.com/mathbot/file/17262837687200yy8mioz.jpg

The inequalities in the image are:

\[
3u - 2 \geq 1 \quad \text{or} \quad 4u - 6 \geq 18
\]

Let’s solve each inequality step by step.

### Solving the first inequality:
\[
3u - 2 \geq 1
\]
1. Add 2 to both sides:
\[
3u \geq 3
\]
2. Divide by 3:
\[
u \geq 1
\]

### Solving the second inequality:
\[
4u - 6 \geq 18
\]
1. Add 6 to both sides:
\[
4u \geq 24
\]
2. Divide by 4:
\[
u \geq 6
\]

### Final Solution:
Since the inequalities are combined with "or," we take the union of the two solutions:
- From the first inequality: \( u \geq 1 \)
- From the second inequality: \( u \geq 6 \)

Therefore, the overall solution is:
\[
u \geq 1
\]

However, since the second inequality requires \( u \geq 6 \), the final answer simplifies to:
\[
u \geq 6
\]

Would you like more details or have any questions?

---

Here are five related questions to consider:
1. What is the difference between "and" and "or" when solving inequalities?
2. How would the solution change if the inequalities were combined with "and" instead of "or"?
3. Can you graph the solution on a number line?
4. What happens if the inequality signs are reversed to \( \leq \)?
5. How do you solve compound inequalities?

**Tip**: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Solve the inequalities: 3u - 2 ≥ 1 or 4u - 6 ≥ 18.

Explore detailed solutions for the inequalities 3u - 2 ≥ 1 and 4u - 6 ≥ 18. This guide offers step-by-step algebraic methods, including addition, subtraction, and division techniques used to isolate the variable. Suitable for high school students learning algebra.

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