# ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Linear Inequations Chapter Test

## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Linear Inequations Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Linear Inequations Chapter Test.

Question 1.

Solve the inequation : 5x – 2 ≤ 3(3 – x) where x ∈ { – 2, – 1, 0, 1, 2, 3, 4}. Also represent its solution on the number line.

Solution:

5x – 2 < 3(3 – x)

=> 5x – 2 ≤ 9 – 3x

=> 5x + 3x ≤ 9 + 2

Question 2.

Solve the inequations :

6x – 5 < 3x + 4, x ∈ I.

Solution:

6x – 5 < 3x + 4

6x – 3x < 4 + 5

=> 3x <9

=> x < 3

x∈I

Solution Set = { – 1, – 2, 2, 1, 0….. }

Question 3.

Find the solution set of the inequation

x + 5 < 2 x + 3 ; x ∈ R

Graph the solution set on the number line.

Solution:

x + 5 ≤ 2x + 3

x – 2 x ≤ 3 – 5

=> – x ≤ – 2

=> x ≥ 2

Question 4.

If x ∈ R (real numbers) and – 1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.

Solution:

– 1 < 3 – 2x ≤ 7

– 1 < 3 – 2x and 3 – 2x ≤ 7

2 x < 3 + 1 and – 2x ≤ 7 – 3

2 x < 4 and – 2 x ≤ 4

x < 2 and – x ≤ 2

and x ≥ – 2 or – 2 ≤ x

x∈R

Solution set – 2 ≤ x < 2

Solution set on number line

Question 5.

Solve the inequation :

(frac { 5x+1 }{ 7 } -4left( frac { x }{ 7 } +frac { 2 }{ 5 } right) le 1frac { 3 }{ 5 } +frac { 3x-1 }{ 7 } ,xin R)

Solution:

(frac { 5x+1 }{ 7 } -4left( frac { x }{ 7 } +frac { 2 }{ 5 } right) le 1frac { 3 }{ 5 } +frac { 3x-1 }{ 7 } )

(frac { 5x+1 }{ 7 } -4left( frac { x }{ 7 } +frac { 2 }{ 5 } right) le frac { 8 }{ 5 } +frac { 3x-1 }{ 7 } )

Question 6.

Find the range of values of a, which satisfy 7 ≤ – 4x + 2 < 12, x ∈ R. Graph these values of a on the real number line.

Solution:

7 < – 4x + 2 < 12

7 < – 4x + 2 and – 4x + 2 < 12

Question 7.

If x∈R, solve (2x-3ge x+frac { 1-x }{ 3 } >frac { 2 }{ 5 } x)

Solution:

(2x-3ge x+frac { 1-x }{ 3 } >frac { 2 }{ 5 } x)

(2x-3ge x+frac { 1-x }{ 3 } ) and (x+frac { 1-x }{ 3 } >frac { 2 }{ 5 } x)

Question 8.

Find positive integers which are such that if 6 is subtracted from five times the integer then the resulting number cannot be greater than four times the integer.

Solution:

Let the positive integer = x

According to the problem,

5a – 6 < 4x

5a – 4x < 6 => x < 6

Solution set = {x : x < 6}

= { 1, 2, 3, 4, 5, 6} Ans.

Question 9.

Find three smallest consecutive natural numbers such that the difference between one-third of the largest and one-fifth of the smallest is atleast 3.

Solution:

Let first least natural number = x

then second number = x + 1

and third number = x + 2

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 5 Linear Inequations Chapter Test are helpful to complete your math homework.

If you have any doubts, please comment below. IMP try to provide online math tutoring for you.

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