Review the solved inequality. What error was made when solving this inequality. What is the correct solution

Question

-4x <32

Answer 1

Let's review the inequality \(-4x < 32\) and go through the steps to solve it.

1. Divide both sides by -4: When we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign.

Starting with: \[ -4x < 32 \]

We divide both sides by -4: \[ x > \frac{32}{-4} \]

So, \[ x > -8 \]

The correct solution is: \[ x > -8 \]

Error Made

If a mistake were made, it likely involved not reversing the inequality sign when dividing by a negative number. If the solution was mistakenly written as \(x < -8\), that would be the error.

Conclusion

The correct solution to the inequality \(-4x < 32\) is indeed: \[ x > -8 \]

Answer 2

Here’s the steps on my problem
-4x<32
-4x/-4< 32/-4
x < -8

Answer 3

Thank you for sharing your steps. It looks like you made an error when dividing both sides of the inequality by \(-4\).

Here's a breakdown of the proper procedure:

1. Starting with the inequality: \[ -4x < 32 \]

2. Dividing both sides by \(-4\): When you divide or multiply both sides of an inequality by a negative number, you need to reverse the inequality sign.

   So, instead of: \[ -4x / -4 < 32 / -4 \] It should be: \[ -4x / -4 > 32 / -4 \]

   This gives: \[ x > -8 \]

Summary of the Solutions

• Your incorrect step led to the conclusion that \(x < -8\), but the correct solution, after reversing the sign when dividing by a negative, is: \[ x > -8 \]

Thank you for double-checking, and I'm glad to clarify that the correct solution is \(x > -8\).