Question

A student solved the inequality as shown to the bottom. what went wrong? give the correct solution set.

4x ≥ -48.
4x/4 ≤ -48/4.
x ≤ -12
Solution set (-[infinity], -12)
What was the student's error?
A. The student reversed the inequality symbol when dividing by a positive number. The direction of the inequality symbol is reversed only when multiplying or dividing by a negative number.
B. The student divided incorrectly. A negative number divided by a positive number is positive, not negative.
C. The student divided incorrectly. The student should have divided both sides of the inequality by -48 .
D. The student did not reverse the inequality symbol when dividing a negative number by a positive number. The direction of the inequality symbol is reversed when dividing a negative number by a positive number.
What is the correct solution set?____(Type your answer in interval notation.)

Answer 1

The student mistakenly reversed the inequality when dividing by a positive number. The correct solution set for the inequality 4x ≥ -48 is [ -12, +infinity ).

Step-by-step explanation:

The student's error was A. The student reversed the inequality symbol when dividing by a positive number. The direction of the inequality symbol is reversed only when multiplying or dividing by a negative number. When dividing both sides of the inequality 4x ≥ -48 by the positive number 4, the direction of the inequality should remain the same. Therefore, the correct solution is:

4x ≥ -48

Dividing by 4: x ≥ -12

The correct solution set in interval notation is [ -12, +infinity ).