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In the inequality 3x + 5 ≤ 2x + 7, after using Rule 1 to move x-terms to one side:
ARule 1 cannot be applied here
B3x - 2x ≤ 7 - 5, i.e. x ≤ 2 (Rule 1 preserves sign; no flip needed)
Cx = 2 only
D3x - 2x ≥ 7 - 5
Answer & Solution
Correct answer: B. 3x - 2x ≤ 7 - 5, i.e. x ≤ 2 (Rule 1 preserves sign; no flip needed)
Rule 1 (adding/subtracting same quantity) preserves the sign. 3x + 5 - 2x - 5 ≤ 2x + 7 - 2x - 5 → x ≤ 2.
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