−3(7x + 11) < 2(2x – 4)
What is the solution set to the inequality?


To solve the inequality \(-3(7x + 11) < 2(2x - 4)\), follow these steps:

1. **Distribute** the constants on both sides:
   \[
   -3 \cdot 7x - 3 \cdot 11 < 2 \cdot 2x - 2 \cdot 4
   \]
   Simplifying this gives:
   \[
   -21x - 33 < 4x - 8
   \]

2. **Move the terms involving \(x\)** to one side and the constant terms to the other side:
   \[
   -21x - 4x < -8 + 33
   \]
   Simplify:
   \[
   -25x < 25
   \]

3. **Divide both sides** by \(-25\) and **reverse the inequality sign** because you're dividing by a negative number:
   \[
   x > \frac{25}{-25}
   \]
   Simplifying further:
   \[
   x > -1
   \]

So, the solution set to the inequality is \(x > -1\).

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

Here are 5 related questions to explore:

1. How do you solve inequalities with multiple steps?
2. What happens to an inequality when you multiply or divide by a negative number?
3. How would the solution change if the inequality were \(-3(7x + 11) \leq 2(2x - 4)\)?
4. How do you represent the solution \(x > -1\) on a number line?
5. How can inequalities be applied in real-world situations?

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

Learn how to solve the inequality -3(7x + 11) < 2(2x - 4) with a detailed step-by-step solution. This problem involves inequalities, the distributive property, and solving equations. Suitable for students in Grades 7-9.

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