We are given the inequality: \[ -4(x + 7) < 3(x - 2) \] Let's solve it step by step to find the equivalent inequality. ### Step 1: Expand both sides We start by expanding both sides of the inequality. On the left side: \[ -4(x + 7) = -4x - 28 \] On the right side: \[ 3(x - 2) = 3x - 6 \] Now the inequality looks like this: \[ -4x - 28 < 3x - 6 \] ### Step 2: Move the variables to one side We move all the terms involving \( x \) to one side and the constants to the other side. First, add \( 4x \) to both sides to move the \( -4x \) term: \[ -28 < 7x - 6 \] Next, add \( 6 \) to both sides to move the constant term: \[ -28 + 6 < 7x \] This simplifies to: \[ -22 < 7x \] ### Step 3: Solve for \( x \) Finally, divide both sides of the inequality by 7: \[ \frac{-22}{7} < x \] Or equivalently: \[ x > \frac{-22}{7} \quad \text{(after flipping the inequality)} \] Thus, the equivalent inequality is: \[ -7x > -34 \] The correct answer is **Option B**. Would you like more details or have any questions? Here are some related questions: 1. What if the inequality sign was \( \leq \) instead of \( < \)? 2. How would the inequality change if we had \( 2(x + 7) \) instead of \( -4(x + 7) \)? 3. What is the geometric interpretation of inequalities on a number line? 4. How would this change if the constants were positive on both sides? 5. Can you check your solution by testing a number for \( x \)? **Tip:** When solving inequalities, if you multiply or divide by a negative number, remember to flip the inequality sign.