Inequalities — Practice Quiz
ICSE · Class 7 · Mathematics
Try a 4-question quiz on Inequalities for ICSE Class 7 Mathematics: tap an answer to check it and see why. 47 questions in the full chapter test.
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Quick Quiz: Inequalities
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Solve the inequation 9(x + 3) - 2 ≥ 2(3x + 4) where x is a negative integer.
Solve 30 - 3(2x - 7) < 13 for x as a positive integer.
Find the solution set of 5x - 12 ≤ 8 when x belongs to the set of integers.
Solve (6x - 2)/5 ≤ 2 when x belongs to the set of whole numbers.
Sample Questions
Find the solution set of -10 < -5 + 2x when x is an integer.
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{..., -2, -1, 0, 1, 2}
Add 5 to both sides: -10 < -5 + 2x ⇒ -5 < 2x. Divide by 2: x > -2.5. For integers, all integers greater than -2.5 are {..., -2, -1, 0, 1, 2}.
Find the solution set of 3x - 8 < 7 when x belongs to the set of natural numbers.
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{1, 2, 3, 4}
Add 8 to both sides: 3x - 8 < 7 ⇒ 3x < 15 ⇒ x < 5. For natural numbers, the values are 1, 2, 3, and 4.
Solve 4x + 5 ≥ 1 when x belongs to the set of whole numbers.
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{0, 1, 2, 3, 4, ...}
Subtract 5: 4x + 5 ≥ 1 ⇒ 4x ≥ -4 ⇒ x ≥ -1. Whole numbers are 0, 1, 2, 3, 4, ... , so every whole number works.
Find the solution set of -2 ≤ x < 2 when x belongs to the set of integers.
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{-2, -1, 0, 1}
The integers must be at least -2 and less than 2. That gives -2, -1, 0, and 1. The number 2 is excluded because the inequality is strict at the upper end.
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