Let's carefully review the steps to identify the mistake in the inequality solving process.
Given inequality:
[tex]\[ -3(2x + 5) < 21 \][/tex]
### Step-by-Step Solution:
Line (1) to Line (2):
Distribute the [tex]\(-3\)[/tex]:
[tex]\[ -3(2x) + (-3)(5) < 21 \][/tex]
This simplifies to:
[tex]\[ -6x - 15 < 21 \][/tex]
This transformation is correct.
Line (2) to Line (3):
Add 15 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ -6x - 15 + 15 < 21 + 15 \][/tex]
This simplifies to:
[tex]\[ -6x < 36 \][/tex]
This transformation is also correct.
Line (3) to Line (4):
Divide both sides by [tex]\(-6\)[/tex]. Note that dividing by a negative number reverses the inequality direction:
[tex]\[ \frac{-6x}{-6} > \frac{36}{-6} \][/tex]
This simplifies to:
[tex]\[ x > -6 \][/tex]
However, in the original line, it is stated as:
[tex]\[ x < -6 \][/tex]
which is incorrect since the inequality sign should flip when dividing by a negative number. This error occurs in this step.
So, the error is found in the step from Line (3) to Line (4).
Conclusion:
The error occurred from line (3) to line (4). The correct solution should have been:
[tex]\[ x > -6 \][/tex]
Therefore, the correct identification of the error is:
The error occurred from line (3) to line (4).
