Mrs. Miller gave the following inequality for her students to solve. 
 
−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:

### Step 1: Distribute the numbers on both sides.
Distribute \(-3\) on the left side and \(2\) on the right side:

\[
-3(7x + 11) = -21x - 33
\]
\[
2(2x - 4) = 4x - 8
\]

So the inequality becomes:
\[
-21x - 33 < 4x - 8
\]

### Step 2: Move the \(x\) terms to one side.
Add \(21x\) to both sides to get all the \(x\) terms on one side:
\[
-33 < 25x - 8
\]

### Step 3: Isolate the \(x\) term.
Add \(8\) to both sides to isolate the \(x\) term:
\[
-25 < 25x
\]

### Step 4: Solve for \(x\).
Divide both sides by \(25\) to solve for \(x\):
\[
x > -1
\]

### Solution:
The solution set to the inequality is:
\[
x > -1
\]

This means \(x\) can be any value greater than \(-1\).

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

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Here are 5 questions to expand your understanding:

1. What would happen if the inequality sign were reversed in the original equation?
2. How would you solve the inequality if the coefficients were fractions instead of whole numbers?
3. Can you explain why we add or subtract the same number from both sides of the inequality?
4. How would the solution change if we multiplied or divided by a negative number?
5. What is the difference between solving inequalities and solving equations?

**Tip:** Remember, when you multiply or divide both sides of an inequality by a negative number, the inequality sign reverses.

Learn how to solve the inequality -3(7x + 11) < 2(2x - 4) with detailed steps and explanations. This problem involves inequalities, distributive property, and solving equations, suitable for Grades 7-9 students.

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