7k + 1 <= 8 or -7 < k - 10 solve inequality

To solve the compound inequality:

\[ 7k + 1 \leq 8 \quad \text{or} \quad -7 < k - 10 \]

We will solve each part separately.

### 1. Solve \( 7k + 1 \leq 8 \):
\[ 7k + 1 \leq 8 \]

Subtract 1 from both sides:
\[ 7k \leq 7 \]

Divide both sides by 7:
\[ k \leq 1 \]

### 2. Solve \( -7 < k - 10 \):
\[ -7 < k - 10 \]

Add 10 to both sides:
\[ 3 < k \]

This can also be written as:
\[ k > 3 \]

### 3. Combine the results:
The solution is \( k \leq 1 \) or \( k > 3 \). 

In interval notation, the solution is:
\[ (-\infty, 1] \cup (3, \infty) \]

Would you like more details or have any questions?

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**Related Questions:**
1. How do you solve compound inequalities involving both "and" & "or"?
2. What is interval notation and how do you use it?
3. How do you graph the solution to a compound inequality on a number line?
4. What is the difference between strict and non-strict inequalities?
5. How do you solve inequalities involving absolute values?

**Tip:** When dealing with inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the compound inequality 7k + 1 <= 8 or -7 < k - 10 step-by-step. This problem involves inequalities, compound inequalities, and interval notation. Suitable for students in Grades 7-9.

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