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To solve the inequality \( -4x + 35 > 2 \), follow these steps:

1. **Subtract 35 from both sides** to isolate the term containing \( x \):
   \[
   -4x + 35 - 35 > 2 - 35
   \]
   Simplifying this, we get:
   \[
   -4x > -33
   \]

2. **Divide by -4** to solve for \( x \). Remember, when you divide or multiply an inequality by a negative number, you must **reverse the inequality sign**:
   \[
   x < \frac{-33}{-4}
   \]
   Simplifying this:
   \[
   x < \frac{33}{4} \quad \text{or} \quad x < 8.25
   \]

So, the solution set for this inequality is \( x < 8.25 \).

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to deepen understanding:
1. How do you handle inequalities when multiplying or dividing by negative numbers?
2. What is the difference between solving equations and solving inequalities?
3. How can you represent the solution \( x < 8.25 \) on a number line?
4. What would the solution set be if the inequality was \( -4x + 35 \geq 2 \)?
5. Can you express this solution set using interval notation?

**Tip:** Always remember to flip the inequality sign when you multiply or divide by a negative number.

Find the solution set of the inequality -4x + 35 > 2.

Learn how to solve the inequality -4x + 35 > 2 with a detailed, step-by-step explanation. Understand the key algebraic concepts and the properties of inequalities, including how to handle negative coefficients. Suitable for students in Grades 7-9.

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