https://file.aiquickdraw.com/mathbot/file/17255763712383to7sew2.jpg

https://file.aiquickdraw.com/mathbot/file/1725576371240bifmsn1x.jpg

Let's solve the inequality from the image.

### Given inequality:
\[
18 > 4 - 7x
\]

### Step 1: Use the addition principle
Subtract \(4\) from both sides to isolate the term involving \(x\):

\[
18 - 4 > 4 - 4 - 7x
\]
\[
14 > -7x
\]

### Step 2: Use the multiplication principle
Now, divide both sides by \(-7\). Remember, when dividing by a negative number, the inequality sign reverses:

\[
\frac{14}{-7} < \frac{-7x}{-7}
\]
\[
-2 < x
\]

This simplifies to:
\[
x > -2
\]

### Final Answer:
The solution set is \( x > -2 \), which matches option **B** in the second image.

Would you like more details on this solution or clarification on the process?

Here are 5 related questions:
1. What is the addition principle in solving inequalities?
2. How does the multiplication principle work when dividing by negative numbers?
3. What would happen if the inequality was reversed, like \( 18 < 4 - 7x \)?
4. Can you explain why the inequality sign flips when dividing by a negative number?
5. How do these principles apply to equalities (i.e., equations)?

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

Solve using the addition and multiplication principles: 18 > 4 - 7x

Learn how to solve the inequality 18 > 4 - 7x step-by-step using the addition and multiplication principles. This problem involves key algebraic concepts such as reversing the inequality sign when dividing by a negative number. Suitable for students in Grades 7-9.

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