Question

Review the solved inequality below. What error was made when solving this inequality? What is the correct solution?
-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 \(-4\).