https://file.aiquickdraw.com/mathbot/file/17281530722741483xzgp.jpg

The given inequality is:

\[
2(n - 2) \geq -28 + 5n
\]

Let's solve it step-by-step:

1. **Expand the left-hand side**:

\[
2(n - 2) = 2n - 4
\]

So the inequality becomes:

\[
2n - 4 \geq -28 + 5n
\]

2. **Rearrange the inequality** to isolate \( n \):

Subtract \( 2n \) from both sides:

\[
-4 \geq -28 + 3n
\]

3. **Add 28 to both sides**:

\[
-4 + 28 \geq 3n
\]

\[
24 \geq 3n
\]

4. **Solve for \( n \)** by dividing both sides by 3:

\[
8 \geq n
\]

This simplifies to:

\[
n \leq 8
\]

### Final Solution:

The solution to the inequality is:

\[
n \leq 8
\]

Would you like more details or have any questions? 

### Related Questions:

1. How would the solution change if the inequality were strict (\(<\) instead of \(\geq\))?
2. What is the solution if the inequality sign is flipped (\(\leq\) becomes \(\geq\))?
3. How do you graph this inequality on a number line?
4. What happens if the coefficient of \( n \) in the equation were negative?
5. How can you check the solution by plugging values back into the original inequality?

### Tip:

Always remember to reverse the inequality sign if you multiply or divide by a negative number while solving inequalities!

Solve the inequality: 2(n - 2) >= -28 + 5n

Learn how to solve the inequality 2(n - 2) >= -28 + 5n step-by-step. This algebra problem involves expanding, simplifying, and isolating variables. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation