Nootan solutions for माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 4 - Linear inequations [Latest edition]

Solve the following inequation and represent the solution on the number line in following case:

4x − 1 > 3

Solve the following inequation and represent the solution on the number line in following case:

5 + 2x > 8 + 5x

Solve the following inequation and represent the solution on the number line in following case:

`(x-1)/3 >= 4`

Solve the following inequation and represent the solution on the number line in following case:

2 − 6x ≤ 7 − 4x

Solve the following inequation and represent the solution on the number line in following case:

`(3x - 2)/5 <= (4x-3)/2`

Solve the following inequation and represent the solution on the number line in following case:

3x + 2 ≤ 5x – (4 – x)

Solve the following inequation and represent the solution on the number line in following case:

`(4-5x)/3 < 2-x`

Solve the following inequation and represent the solution on the number line in following case:

`(2-x)/2 + (4-2x)/3>0`

Solve the following inequation and represent the solution on the number line in following case:

−(x − 3) + 4 < −2x + 5

Solve the following inequation and represent the solution on the number line in following case:

`(4-2x)/3 >= x/2 - 3`

Solve the following inequation and represent the solution on the number line in following case:

2x + 33 ≥ 38, 3x + 1 ≤ 12

Solve the following inequation and represent the solution on the number line in following case:

3x − 7 ≤ 5, 2x − 7 < 7

Solve the following inequation and represent the solution on the number line in following case:

3x + 2 ≥ 8, 2x + 1 ≤ 12

Solve the following inequation and represent the solution on the number line in following case:

4x − 7 > 2x + 3, `(x-1)/3 < (x-3)/5`

Solve the following inequation and represent the solution on the number line in following case:

x + 2 ≤ 5, 3x − 4 > −2 + x

If the replacement set is the set of whole numbers, find the solution set:

8 + 2x ≤ 28 − 3x

If the replacement set is the set of integers, find the solution set:

`x - 5/2 <= 3/2 - x`

If the replacement set is {1, 2, 3, 4, 5, 6, 7, 8}, find the solution of 2 (x − 4) < 1.

If the replacement set is the set of odd natural numbers, then solve:

5x − 17 ≤ x + 9

If A = {x : 11x – 5 > 7x + 3, x ∈ R} and B = {x : 15 + 12x ≤ 18x – 9, x ∈ R}, find the range of set A ∩ B and represent it on the number line.

Solve: `(3x)/5 + 2 < x+4<= x/2 + 5, x ∈ R` and represent the solution set on the number line.

Solve: 11x − 4 < 15x + 4 ≤ 13x + 14, x ∈ W and represent the solution set on a real number line.

The temperature in degree Fahrenheit (°F) ranges between 86 and 95 on a certain island. Celsius temperature (°C) is related to Fahrenheit temperature by the formula `C = 5/9 (F-32)`. What is the Celsius temperature range of this island?

The water acidity in a swimming pool is considered normal when the average pH level of three daily measurements is between 7.2 and 7.8. If first two pH readings are 7.48 and 7.82, find the range of pH value for the third day so that the acidity level is within the normal range.

Find all pairs of consecutive even positive integers, both of which are larger than 8, such that their sum is less than 25.

In the first four examinations, each of 100 marks, Hamid got 94, 73, 72 and 84 marks. If a final average greater than or equal to 80 and less than 90 is needed to obtain a final grade B in a course, what range of marks in the fifth (last) examination will result in Hamid receiving ‘B’ in the course?

The marks obtained by a student in two tests were 70 and 75. Find the minimum marks he should get in the third test to have an average of at least 60 marks.

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

An integer is such that one-fouth of the next integer is atleast one more than one-fifth of the previous integer. Find the smallest value of the integer.

Solve the following inequation, write down the solution set and represent it on the number line.

`-3 + x <= 7x/2 + 2 < 8+2x, x∈l`

The solution set for the inequation 2x + 4 ≤ 14, x ∈ W is ______.

If 3x – 4 ≤ 10 and replacement set is the set of natural numbers then solution set is ______.

If 5x − 3 < 10 and 1 − 2x < −7, then solution set is:

The solution set for inequation 3(7 − x) ≥ 15 − 7x > `(x+1)/3, x ∈ R` is ______.

For the inequation, `4x - 19< (3x)/5 -2 <= -2/5 + x, x ∈ R` the solution set is ______.

The solution of the inequation, `2x - 7/2 > 5/2 - x, x ∈ N,` is ______.

If `x + x/2 + x/3 > 11, x ∈ R` then one solution of the inequation is ______.

If `(3x)/5 - (2x-1)/3 > 1, x ∈ l` then solution set is ______.

Assertion: The solution set of 7 + 3x ≤ 35 − 2x, x ∈ W is {0, 1, 2, 3, 4, 5}

Reason: W = {0, 1, 2, 3, 4, ...}

Assertion: `(x-2)/3 >= 2, x ∈ R` gives x ≥ 8.

Reason: a > b ⇒ −a < −b

Assertion: `-8 1/2 < - 1/2 -4x <= 7 1/2, x ∈ l` gives x ∈ (−2, −1, 0}

Reason: The set from which the values of the variable involved in the equation are chosen, is called the replacement set.

Assertion: If the same number or expression is added to both sides of an inequation, the resulting inequation has the same sign of inequality as that of the original.

Reason: −5 (x − 9) ≥, 17 − 9x > x + 2, x ∈ R gives Х ∈ `[-7, -3/2]`

In the following questions, two statements (i) and (ii) are given. Choose the valid statement.

1. The smallest whole number is 1.
2. 5x + 3 ≥ 11, x ∈ N gives x = {2, 3, 4, 5, ...}.

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. 3x + 1 ≤ 17, then greatest natural number satisfying this inequation is 5.
2. 1 − 3x ≤ 2x − 3, then least integer value of x is 1.

In the following questions, two statements (i) and (ii) are given. Choose the valid statement.

1. a > ba + c > b + c
2. a > b ⇒ −a > −b

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. 4x + 1 ≤ x + 10 gives x ≥ 3.
2. 3x − 1 > x gives x > `-1/2`

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.

Solve −12 < `(4-3x)/-5 <2, x ∈ R` and represent the solution on the number line.

Solve `-15 < (3(x-2))/5 <= 0,` x ∈ R and represent the solution on the number line.

A solution in kept between 68°F and 77°F. What is the range of temperature in degree celsius (C), if the Celsius/Fahrenheit (F) conversion formula is F = `9/5` C + 32?

A solution set of 7x − 1 > 4x + 3 and B is the solution set of 5x – 1 ≥ 2 (x + 4) where x ∈ W, find A ∩ B.

Solve: 2 (x − 3) – 7 (x + 5) ≤ 3x – 9 and (x + 5) – 7 (x – 2) ≥ 4x + 9, x ∈ R and represent the solution on the number line.

Solve: `-x/3 <= x/2 - 1 1/3 < 1/6`, x ∈ R and represent the solution on the number line.

If the replacement set is the set of even natural numbers, then solve `(5x-8)/3 <= (7x+13)/5 - x/2`

If P = {x : 3x + 4 ≤ 23, x ∈ N} and Q = {x : −6 ≤ 2x + 2 < 9, x ∈ I} find PQ.

Solve: `-2 2/3 <= x + 1/3 < 3 1/3`, x ∈ R and represent the solution on the number line.