Question

Find the student’s error in solving the following inequality.
2 < –3x –4 < 5
6 < –3x < 5
–2 > x > –5/3

Answer 1

The student didn't add 4 to all expressions in the inequality.
It should be:
$2<-3x-4<5 \ \ \ |+4 \\ 6<-3x<9 \ \ \ |\div (-3) \\ -2>x>-3$

Answer 2

2 < -3x - 4 < 2
+4        +4  +4
2 < -3x < 6
-2           -2
       -3x < 4
        -3    -3
          x < -1 1/3

6 < -3x < 5
-5           -5
1 < -3x
-3    -3
-1/3 < x
x > -1/3

-2 > x > -5/3
+5/3      +5/3
-1/3 > x
x < -1/3