Solve the following inequality for x. -16(x - 3) < -128

Answer 1

To solve the inequality \(-16(x - 3) < -128\), we can start by dividing both sides of the inequality by \(-16\). Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.

1. Rewrite the inequality: \[ -16(x - 3) < -128 \]

2. Divide both sides by \(-16\) and reverse the inequality sign: \[ x - 3 > \frac{-128}{-16} \]

3. Calculate \(\frac{-128}{-16}\): \[ \frac{-128}{-16} = 8 \]

4. So the inequality becomes: \[ x - 3 > 8 \]

5. Add \(3\) to both sides: \[ x > 8 + 3 \]

6. Simplify: \[ x > 11 \]

Thus, the solution to the inequality is: \[ \boxed{x > 11} \]