m+5>\:11\:or\:8-10m\ge 33\:in\:interval\:notation

Let's solve the system of inequalities one by one and then express the solution in interval notation.

### 1. Solving \( m + 5 > 11 \):

Subtract 5 from both sides:
\[
m > 11 - 5
\]
\[
m > 6
\]

### 2. Solving \( 8 - 10m \geq 33 \):

Subtract 8 from both sides:
\[
-10m \geq 33 - 8
\]
\[
-10m \geq 25
\]

Now, divide both sides by \(-10\). When dividing by a negative number, the inequality sign flips:
\[
m \leq \frac{25}{-10}
\]
\[
m \leq -2.5
\]

### 3. Combining the Solutions:

We have two inequalities:
1. \( m > 6 \)
2. \( m \leq -2.5 \)

Since these are conflicting (there is no overlap between \( m > 6 \) and \( m \leq -2.5 \)), there is **no solution**. 

### 4. Interval Notation:

Since no values of \( m \) can satisfy both inequalities, the solution in interval notation is:
\[
\boxed{\varnothing}
\]
This means the solution set is empty.

Would you like more details on any step or further clarification?

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Here are 5 related questions for practice:
1. Solve \( 2m + 7 > 13 \) and express in interval notation.
2. Solve \( 4 - m \leq 2m + 10 \) and express in interval notation.
3. What is the solution to \( 3m + 2 < 5m - 7 \)?
4. How do you solve \( 5 - 2m \geq m + 8 \)?
5. Solve and express in interval notation: \( m - 5 > 2 \) or \( m + 6 \leq 3 \).

**Tip:** Always remember to reverse the inequality sign when dividing or multiplying by a negative number!

m + 5 > 11 or 8 - 10m ≥ 33 in interval notation

Learn how to solve the system of inequalities m + 5 > 11 or 8 - 10m ≥ 33 step by step. This problem involves solving linear inequalities, understanding how to handle inequalities with negative numbers, and expressing solutions in interval notation. Suitable for students in Grades 9-11.

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