https://file.aiquickdraw.com/mathbot/file/17271018248572kf3v1z2.jpg

The image contains the following system of inequalities:

\[
-5(n - 1) \leq 35 \quad \text{or} \quad 3 + n < 10
\]

Let's solve each inequality step-by-step:

### Solving the first inequality: \(-5(n - 1) \leq 35\)

1. Distribute the \(-5\) on the left-hand side:
   \[
   -5n + 5 \leq 35
   \]

2. Subtract 5 from both sides:
   \[
   -5n \leq 30
   \]

3. Divide both sides by \(-5\), and remember to **reverse the inequality** since we're dividing by a negative number:
   \[
   n \geq -6
   \]

### Solving the second inequality: \(3 + n < 10\)

1. Subtract 3 from both sides:
   \[
   n < 7
   \]

### Combining the solutions:

The solution is:
\[
n \geq -6 \quad \text{or} \quad n < 7
\]

In interval notation:
\[
n \in [-6, \infty) \quad \text{or} \quad n \in (-\infty, 7)
\]

Since the union of these intervals covers all real numbers, the solution is:
\[
n \in \mathbb{R}
\]

Would you like more details or have any other questions?

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Here are 5 related questions:
1. What happens if both inequalities are combined with "and" instead of "or"?
2. How do you represent strict inequalities in interval notation?
3. What is the significance of reversing the inequality when dividing by a negative number?
4. How would you solve these inequalities graphically?
5. What real-world problems can be modeled using inequalities?

**Tip:** When solving inequalities, always pay attention to whether you're multiplying or dividing by negative numbers, as it will flip the inequality sign!

Solve the following system of inequalities: -5(n - 1) ≤ 35 or 3 + n < 10.

Learn how to solve the system of inequalities -5(n - 1) ≤ 35 or 3 + n < 10. This problem involves the distributive property and inequality operations. Suitable for students in Grades 8-10.

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