Error: See solution. Correct Solution: - 1/2 > x > - 3 Graph:
Practice makes perfect
To locate the error, we can analyze each step of the work to ensure it is mathematically correct. From the first line to the second, we notice that there is an attempt to subtract 3.
4 < -2 x& + 3 < 9
⇓
4 < -2 x& < 6 *This was done from the middle and from the right-hand side, but not from the left-hand side. This is the error. Inverse operations need to be applied to all sides of the compound inequality.
Since the original answer was incorrect, the graph is also incorrect. To graph the correct solution, we will place open circles at both - 12 and - 3, and shade the region between them.
