Review the solved inequality below. What error was made when solving this inequality? What is the correct solution? -4x/-4 < 32/-4 = x<-8

Answer 1

Let's analyze the inequality step by step.

The inequality provided is:

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

First, simplifying both sides:

1. For the left side: \(\frac{-4x}{-4} = x\)

2. For the right side: \(\frac{32}{-4} = -8\)

So we rewrite the inequality as:

\[ x < -8 \]

This means that \(x\) is less than \(-8\).

However, you wrote the wrong final expression as \(x < -8 = x < -8\). The mistake here implies that we are leaving the inequality sign in the wrong direction.

The correct interpretation is just as we simplified it above:

The correct solution to the inequality \(-4x < 32\) (which is what we started with) after division by \(-4\) should have the inequality sign flipped (since we are dividing by a negative number).

So, indeed, when dividing both sides of an inequality by a negative number, you must reverse the inequality sign.

Thus, the corrected inequality after solving should have been:

\[ x > -8 \]

Correct Solution: The correctly solved inequality is:

\[ x > -8 \]