https://file.aiquickdraw.com/mathbot/file/1729544725418doh60xsj.jpg

Let's solve the inequality step-by-step.

The inequality is:
\[
14 < -6n - 10
\]

### Step 1: Isolate the term with \( n \)
To isolate \( -6n \), first add 10 to both sides of the inequality:
\[
14 + 10 < -6n
\]
\[
24 < -6n
\]

### Step 2: Solve for \( n \)
Now, divide both sides of the inequality by \( -6 \). **Remember that dividing by a negative number reverses the inequality sign**:
\[
\frac{24}{-6} > n
\]
\[
-4 > n
\]
This can also be written as:
\[
n < -4
\]

### Solution:
The solution to the inequality is \( n < -4 \).

### Graphing:
The graph shows the interval \( n < -4 \), which means all values less than -4. On the number line, this is represented by an open circle at \( -4 \) and an arrow extending to the left (towards negative infinity).

### Do you want further details or explanations?

Here are five related questions:
1. How would the solution change if the inequality were \( 14 > -6n - 10 \)?
2. What happens to the inequality when multiplying by negative numbers?
3. How would the graph look if the inequality were \( n \geq -4 \)?
4. Can you explain why we reverse the inequality when dividing by a negative number?
5. What is the solution for \( 14 \leq -6n - 10 \)?

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

Solve the inequality: 14 < -6n - 10 and graph the solution.

Learn how to solve and graph the linear inequality 14 < -6n - 10. This step-by-step guide covers algebraic manipulation, inequality properties, and graphing solutions on the number line. Suitable for students in Grades 8-10.

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