alleryIn 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.
Keep practising Linear Inequalities
Browse all Linear Inequalities questions for AP Intermediate 1st Year, or explore more Mathematics topics.
Related questions
600 L of 12% acid has x L of 30% acid added to give a mixture between 15% and 18% acid. FiFor pieces x, x + 3 and 2x, the third must be at least 5 cm longer than the second. The lePieces of lengths x, x + 3 and 2x are cut from a 91 cm board. What is the greatest whole vLongest side is 3 times the shortest; third is 2 cm less than longest. Perimeter is at leaFive exams average at least 85 needed. Marks so far are 84, 90, 92 and 94. What least markWhich is the solution of 5x - 3 > 3x - 5?Solve 37 - (3x + 5) > 9x - 8(x - 3) for real x.Solve 2(2x + 3) - 10 < 6(x - 2) for real x.