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

Question

-4x < 32
----- ----
-4 -4
x<-8

Answer 1

The solved inequality you provided is:

\[ -4x < 32 \]

When dividing both sides of an inequality by a negative number, the direction of the inequality must change. In this case, \(-4\) is negative, so when dividing both sides by \(-4\), the inequality sign should flip.

The correct steps to solve the inequality are:

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

2. Divide both sides by \(-4\), remembering to flip the inequality: \[ x > \frac{32}{-4} \]

3. Simplify the right side: \[ x > -8 \]

So, the correct solution is:

\[ x > -8 \]

The error in your original solution was not flipping the inequality sign when dividing by \(-4\).