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

Question

-4x/-4 < 32/-4
x<-8
*Your response is worth 2 points! 1 point for correctly identifying the error, and 1 point for providing the correct solution.
The error in the solved inequality is in the simplification of the left side. When dividing by -4, the direction of the inequality should reverse since we are dividing by a negative number.

The original inequality was: [ \frac{-4x}{-4} < \frac{32}{-4} ] This simplifies to: [ x < -8 ] But because we divided by a negative number (-4), the correct inequality should actually be: [ x > -8 ]

So, the correct solution is: [ x > -8 ]

Answer 1

You correctly identified the error in the solving process. When dividing an inequality by a negative number, the direction of the inequality must be reversed.

The original inequality was:

\[ \frac{-4x}{-4} < \frac{32}{-4} \]

Simplifying this gives:

\[ x < -8 \]

However, since we divided both sides by -4, we should have reversed the inequality sign. Therefore, the correct form is:

\[ x > -8 \]

So, the correct solution is indeed:

\[ x > -8 \]

In summary:

1. The error was not reversing the inequality when dividing by -4.
2. The correct solution is \( x > -8 \).