https://file.aiquickdraw.com/mathbot/file/1725978292676wkjt1trr.jpg

Let's solve the compound inequality:

### First inequality:
\[
3u - 5 \geq 10
\]
Solve for \( u \):

1. Add 5 to both sides:
\[
3u \geq 15
\]

2. Divide both sides by 3:
\[
u \geq 5
\]

### Second inequality:
\[
2u + 4 < 6
\]
Solve for \( u \):

1. Subtract 4 from both sides:
\[
2u < 2
\]

2. Divide both sides by 2:
\[
u < 1
\]

### Compound inequality:
The compound inequality involves **"or"**, so we take the union of the two solutions:

- From the first inequality, \( u \geq 5 \).
- From the second inequality, \( u < 1 \).

Since there is no overlap between these two conditions, the solution is the union of the intervals \( (-\infty, 1) \cup [5, \infty) \).

### Final answer in interval notation:
\[
(-\infty, 1) \cup [5, \infty)
\]

Let me know if you would like further details, and here are a few related questions you might consider:

1. How do you solve compound inequalities involving "and" instead of "or"?
2. What is the difference between strict inequalities and inclusive inequalities in interval notation?
3. How can you verify the solution of a compound inequality?
4. What are the steps to solving inequalities with more than one variable?
5. How would the solution change if it were \( u + 5 \geq 10 \) instead of \( 3u - 5 \geq 10 \)?

**Tip:** When solving inequalities, always pay attention to whether you need to flip the inequality sign, especially when multiplying or dividing by negative numbers.

Solve the compound inequality: 3u - 5 ≥ 10 or 2u + 4 < 6. Write the solution in interval notation. If there is no solution, enter ∅.

Learn how to solve the compound inequality 3u - 5 ≥ 10 or 2u + 4 < 6 and express the solution in interval notation. This algebra problem covers key concepts in inequalities and union of intervals, suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation