Let's carefully analyze each step to understand where the error occurs.
### Step-by-Step Solution:
Given Inequality:
[tex]\[ -3(2x + 5) < 21 \][/tex]
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From Line (1) to Line (2):
Starting with:
[tex]\[ -3(2x + 5) < 21 \][/tex]
Distribute [tex]\(-3\)[/tex] across the parentheses:
[tex]\[ -6x - 15 < 21 \][/tex]
So, Line (2) [tex]\[ -6x - 15 < 21 \][/tex] is correct.
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From Line (2) to Line (3):
To isolate the term with [tex]\(x\)[/tex], add 15 to both sides of the inequality:
[tex]\[ -6x - 15 + 15 < 21 + 15 \][/tex]
[tex]\[ -6x < 36 \][/tex]
So, Line (3) [tex]\( -6x < 36 \)[/tex] is correct.
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From Line (3) to Line (4):
Now, divide both sides of the inequality by [tex]\(-6\)[/tex]. Remember, dividing by a negative number reverses the inequality sign:
[tex]\[ \frac{-6x}{-6} > \frac{36}{-6} \][/tex]
[tex]\[ x > -6 \][/tex]
This means Line (4) should be [tex]\( x > -6 \)[/tex], not [tex]\( x < -6 \)[/tex].
Therefore, the error occurs from Line (3) to Line (4).
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### Conclusion:
The correct identification of where the error occurred is:
The error occurred from Line (3) to Line (4).
