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

−3(7*x* + 11) < 2(2*x* – 4)

What is the solution set to the inequality?

A.*x* > 3

B.*x* < 1

C.*x* < 2

D.*x* > −1

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

### Step 1: Expand both sides of the inequality
Distribute the numbers outside the parentheses on both sides:

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

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

### Step 2: Move the variable terms to one side
Add \(21x\) to both sides to move all terms with \(x\) to the right:
\[
-33 < 25x - 8
\]

### Step 3: Move the constant terms to the other side
Add 8 to both sides:
\[
-33 + 8 < 25x
\]
\[
-25 < 25x
\]

### Step 4: Solve for \(x\)
Now, divide both sides by 25:
\[
x > -1
\]

### Final Answer:
The solution set is \(x > -1\), which corresponds to option **D**.

Would you like more details on any step? Here are 5 related questions:

1. How would the solution change if the inequality were \(> \) instead of \(<\)?
2. What happens when the coefficient of \(x\) is negative?
3. How do you solve inequalities involving fractions?
4. What is the significance of switching the inequality sign when multiplying or dividing by a negative number?
5. How can inequalities be graphed on a number line?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

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

−3(7*x* + 11) < 2(2*x* – 4)

What is the solution set to the inequality?

A. *x* > 3
B. *x* < 1
C. *x* < 2
D. *x* > −1

Learn how to solve the linear inequality −3(7x + 11) < 2(2x – 4) step by step. This problem involves expanding brackets, combining like terms, and solving for x. It covers core algebra concepts and is ideal for students in Grades 7-9.

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