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Let's solve the compound inequality step by step.

The given inequalities are:

1. \( 4u - 2 \geq -14 \)
2. \( 3u - 5 \leq 10 \)

### Step 1: Solve Each Inequality Separately

#### Solving \( 4u - 2 \geq -14 \):

1. Add 2 to both sides:
   \[
   4u \geq -12
   \]
2. Divide both sides by 4:
   \[
   u \geq -3
   \]

#### Solving \( 3u - 5 \leq 10 \):

1. Add 5 to both sides:
   \[
   3u \leq 15
   \]
2. Divide both sides by 3:
   \[
   u \leq 5
   \]

### Step 2: Combine Solutions

We have:

- \( u \geq -3 \)
- \( u \leq 5 \)

Since this is a compound inequality involving "or", we take the union of these two inequalities. This means \( u \) can be in either of these ranges.

### Step 3: Write the Solution in Interval Notation

The solution for \( u \geq -3 \) and \( u \leq 5 \) is:

\[
u \in [-3, 5]
\]

Thus, in interval notation, the solution is:

\[
[-3, 5]
\]

### Summary
The interval notation for the solution is: **[-3, 5]**.

Would you like more details or have any questions about the steps involved?

Here are some related questions you might find helpful:
1. How do you solve compound inequalities involving "and"?
2. What is the difference between "and" and "or" in inequalities?
3. How can I graph the solution of an inequality on a number line?
4. How do you convert a compound inequality to interval notation?
5. What are some common mistakes to avoid when solving inequalities?

**Tip:** Always remember that for compound inequalities involving "or," you take the union of all possible solutions, which means the solution includes any value that satisfies either inequality.

Solve the compound inequality 4u - 2 ≥ -14 or 3u - 5 ≤ 10. Write the solution in interval notation.

Learn how to solve the compound inequality 4u - 2 ≥ -14 or 3u - 5 ≤ 10, and write the solution in interval notation. This problem covers key algebraic concepts and techniques for solving inequalities, suitable for Grades 8-10.

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