The mistake was made during the distribution step from line (1) to line (2), where -3 times 5 was incorrectly noted as +15 instead of the correct -15.
The error occurred from line (2) to line (3).
In line (2), the student incorrectly distributed the negative sign inside the parentheses and simplified it, resulting in -6x < 21.
However, in line (3), the student incorrectly wrote the inequality as -6x < 36 instead of -6x < 21. This error led to the incorrect conclusion in line (4), which should be x > -6 instead of x < -6.
The error occurred from line (2) to line (3). When you distribute the -3 across the terms in the parenthesis in line (1), the result should be -6x - 15 < 21. Then, when you add 15 to both sides to isolate the term with x, you should end with -6x < 36, which is correctly shown in line (3). However, the error in line (2) is a matter of an incorrect distribution where -3 times 5 was incorrectly written as +15 rather than -15, affecting all subsequent steps.