Class X ICSE Maths Chapter Linear Inequalities Exercise 4
Welcome to our comprehensive collection of questions on "Linear Inequalities," designed to enhance your understanding of this important topic in mathematics. Our question bank covers a wide range of concepts, including graphing linear inequalities, solving systems of inequalities, and real-world applications. These practice questions are perfect for students looking to strengthen their skills in interpreting and solving inequalities, whether in preparation for exams or to deepen their overall math knowledge. With a variety of question types and difficulty levels, our resource is the ideal platform for mastering "Linear Inequalities."
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Q1 Solve the inequation 3x -11 < 3, where x ∈ {1, 2, 3,.., 10}.Also represent its solution on a number line
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Q4 List the solution set of 30-4(2x - 1) < 30, given that x is a positive integer.
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Q7 Solve x - 3 (2 + x) > 2(3x - 1), x ∈ {-3, -2, -1, 0, 1, 2}. Also represent its solution on the number line.
Q11 Find the values of x, which satisfy the inequation:
-2 ≤ 1 / 2 - 2x / 3 ≤ 1 5 / 6 , x ∈ N.
Graph the solution set on the number line.
Q12 If x ∈ W, find the solution set of 3/5x – (2x – 1)/3 > 1. Also graph the solution set on the number line, if possible.
Q14 Given that x ∈ I, solve the inequation and graph the solution on the number line:
3 ≥ (x – 4)/2 + x/3 ≥ 2
Q16 If x ∈ Z, solve 2 + 4x < 2x – 5 ≤ 3x. Also represent its solution on the number line.
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Q17 Solve: (4x – 10)/3 ≤ (5x – 7)/2, x ∈ R and represent the solution set on the number line.
Q18 Solve 3x/5 – (2x – 1)/3 > 1, x ∈ R and represent the solution set on the number line.
Q19 Given that x ∈ R, solve the following inequation and graph the solution on the number line: -1 ≤ 3 + 4x < 23.
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Q20 Solve the following inequation and graph the solution on the number line.
-2 2/3 ≤ x+ 1/3 < 3+1/3 ,x ∈ R
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Q21 Solve the following inequation and represent the solution set on the number line:
-3 ≤ <-1 /2 -2x/3 ≤ 5/6,x ∈R
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Q22 Solving the following inequation, write the solution set and represent it on the number line
-3(x – 7) ≥ 15 – 7x > x+1 / 3 , x ∈ R
Q23 Solve the following inequation, write down the solution set and represent it on the real number line:
-2 + 10x ≤ 13x + 10 ≤ 24 + 10x, x ∈ Z
Q24 Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.
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Q25 If x ∈ I, A is the solution set of 2 (x – 1) < 3x – 1 and B is the solution set of 4x – 3 ≤ 8 + x, find A ∩ B.
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Q26 If P is the solution set of -3x + 4 < 2x – 3, x ∈ N and Q is the solution set of 4x – 5 < 12, x ∈ W, find - P ∩ Q
- Q – P
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Q27 A = {x : 11x – 5 > 7x + 3, x ∈ R} and
B = {x : 18x – 9 ≥ 15 + 12x, x ∈ R}
Find the range of set A ∩ B and represent it on a number line
Q28 Given: P {x : 5 < 2x – 1 ≤ 11, x ∈ R}
Q {x : – 1 ≤ 3 + 4x < 23, x ∈ I} where
R = (real numbers), I = (integers)
Represent P and Q on number line. Write down the elements of P ∩ Q.
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Q29 If x ∈ I, find the smallest value of x which satisfies the inequation 2x+5/2 > 5x/3 +2
Q30 Given 20 – 5 x < 5 (x + 8), find the smallest value of x, when - x ∈ I
- x ∈ W
- x ∈ N
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Q31 Solve the following inequation and represent the solution set on the number line:
4x – 19 < 3x/5 – 2 ≤ -2/5 + x, x ∈ R
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Q32 Solve the given inequation and graph the solution on the number line:
2y – 3 < y + 1 ≤ 4y + 7;
y ∈ R.
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Q33 Solve the inequation and represent the solution set on the number line.
-3 + x ≤ 8x/3 + 2 ≤ 14/3 + 2x,
where x ∈I
Q34 Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.
Q35 One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres. Find the length of the shortest pole.
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