Class 10 ICSE Maths Linear Inequations Important Questions

In Mathematics, inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

Class 10 ICSE Linear Inequations Important Questions

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Board Questions
Important Questions





Linear Inequations Important Questions

Q1 Given x € (-3, -4, -5, - 6) and 9 ≤ 1 – 2x, find the possible values of x. Also represent its solution set on the number line.

Solution

Q2 Solve the inequation 3 - 2x ≥ x – 12, given that x € N.

Solution

Q3 If x € W, find the solution set of
3 / 5
x -
2x-1 / 3
> 1

Solution

Q4 Find the values of x, which satisfy the inequation -2
5 / 6
<
1 / 2
-
2x / 3
≤ 2, x € W. Graph the solution set on the number line.

Solution

Q5 Solve
2x+1 / 3
≥
3x-2 / 5
, x € R. Graph the solution set on the number line .

Solution

Q6 Find the range of values of x, which satisfy the inequation -
1 / 5
≤
3x / 10
+1 <
2 / 5
, x € R. Graph the solution set on the number line .

Solution

Q7 P is the solution set of 8x-1> 5x+2 and Q is the solution set of 7x-2 ≥ 3(x+6), where x € N. Find the set P ∩ Q.

Solution

Q8 Solve the following inequation, write the solution set and represent it on the number line : -
x / 3
≤
x / 2
- 1
1 / 3
<
1 / 6
, x € R

Solution

Q9 John needs a minimum of 360 marks in four tests in a Mathematics course to obtain an A grade. On his first three tests, he scored 88, 96, 79 marks. What should his score be in the fourth test so that he can make an A grade?

Solution

Q10 An integer is such that one-third of the next integer is atleast 2 more than one-fourth of the previous integer. Find the smallest value of the integer.

Solution

Q11 Find three largest consecutive natural numbers such that the sum of one-third of first, one-fourth of second and one-fifth of the third is atmost 25.

Solution

Q12 Solve the inequation and graph the solution on the number line : 2y-3 < y+1 ≤ 4y+7 ; y € R.

Solution

Q13 Solve the inequation and represent the solution set on the number line : -3 + x ≤
8x / 3
+ 2 ≤
14 / 3
+2x , where x € I.

Solution

Q14 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.

Solution

Q15 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.

Solution

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