# Linear Equations Class-7 ML Aggarwal ICSE Maths Solutions

Linear Equations Class-7 ML Aggarwal ICSE Mathematics Solutions Chapter-9. We provide step by step Solutions of Exercise / lesson-9 Linear Equations and Inequalities ICSE Class-7th ML Aggarwal Maths.

Our Solutions contain all type Questions with Exe-9.1 , Exe-9.2, Exe-9.3 Objective Type Questions ( including Mental Maths Multiple Choice Questions Value Based Questions, HOT) and Check Your Progress to develop skill and confidence. Visit official Website for detail information about ICSE Board Class-7 Mathematics.

## Linear Equations Class-7 ML Aggarwal ICSE Mathematics Solutions with Inequalities Chapter-9

–: Select Topic :–

Exercise 9.1 ,

Exercise-9.2,

Exercise-9.3,

Objective Type Questions, Mental Maths,

Multiple Choice Questions ,(MCQ)

Value Based Question

HOTS

### Exercise-9.1, Linear Equations and Inequalities Class-7 ML Aggarwal ICSE Mathematics Solutions

Solve the following ( 1 to 9 ) equations

Question 1

(i) 2 (3-2x) =13

(ii)……….

Question 2

(i)……….

(ii)……….

Question 3

(i)……….

(ii)……….

Question 4

(i)……….

(ii)……….

Question 5

(i)……….

(ii)……….

Question 6

(i)……….

(ii)……….

Question 7

(i)……….

(ii)……….

Question 8

(i)……….

(ii)……….

Question 9

(i)……….

(ii)……….

Question 10

Find the value of p if the value of

………………….

### Linear Equations and Inequalities Class-7 ML Aggarwal ICSE Mathematics Solutions Exercise- 9.2

Question 1 and Question 2

If 7 is added to five times a number, the result is 57. Find the number.

Question 3

A number is as much greater than 15 as it is less than 51. Find the number.

Let the number be x

Question 4

if $\frac { 1 }{ 2 }$ is subtracted from a number and the difference is multiplied by 4, the result is 5. What is the number?

Question 5

The sum of two numbers is 80 and the greater number exceeds twice the smaller by 11. Find the numbers.

Smaller number = 23
Greater number = 2x + 11 = 2 × 23 + 11 = 46 + 11 = 57

Question 6

Find three consecutive odd natural numbers whose sum is 87

Question 8

A chair costs ₹ 250 and the table costs ₹ 400. If a housewife purchased a certain number of chairs and two tables for ₹ 2800, find the number of chairs she purchased.

Question 9

Aparna got ₹ 27840 as her monthly salary and over-time. Her salary exceeds the overtime by ₹ 16560. What is her monthly salary?

Question 11

A purse contains ₹ 550 in notes of denominations of ₹ 10 and ₹ 50. If the number of ₹ 50 notes is one less than that of ₹ 10 notes, then find the number of ₹ 50 notes.

Question 14

The length of a rectangle plot is 6 m less than thrice its breadth. Find the dimensions of the plot if its perimeter is 148 m.

### ML Aggarwal ICSE Mathematics Solutions Exercise- 9.3, Linear Equations and Inequalities Class-7

Question 1

if the replacement set is (- 5, – 3, – 1, 0, 1, 3, 4), find the solution

set of:
(i) x < -2
(ii) x > 1
(iii) x ≥ -1
(iv) -5 < x < 3
(v) -3 ≤ x < 4
(vi) 0 ≤ x < 7

Replacement set = {-5, -3, -1, 0, 1, 3, 4}
(i) Solution set of x < – 2 = {-5, -3}
(ii) Solution set of x > 1 = {3, 4}
(iii) Solution set of x ≥ -1 = {- 1, 0, 1, 3, 4}
(iv) Solution set of -5 < x < 3 = {-3, -1, 0, 1}
(v) Solution set of -3 ≤ x < 4 = {-3, -1,0, 1, 3}
(vi) Solution set of 0 ≤ x < 7 = {0, 1, 3, 4}

Question 2

Represent the following inequations graphically:

(i) x ≤ 3, x ∈ N
(ii) x < 4, x ∈ W
(iii) -2 ≤ x < 4, x ∈ I
(iv) -3 ≤ x ≤ 2, x ∈ I

Question 3

Solve the following inequations.
(i) 4 – x > -2, x ∈ N
(ii) 3x + 1 ≤ 8, x ∈ W
Also represent their solutions on the number line

Question 5

Solve -7 < 4x + 1 ≤ 23, x ∈ I.

Objective Type Questions

#### Mental Maths, Linear Equations Class-7 ML Aggarwal ICSE Mathematics Solutions Chapter-9

Question 1

Fill in the blanks:
(i) A linear equation in one variable cannot have more than ………… solution.
(ii) If five times a number is 50, then the number is ……….
(iii) The number 4 is the ………. of the equation 2y – 5 = 3.
(iv) The equation for the statement ‘5 less than thrice a number x is 7’ is ……….
(v) …………. is a solution of the equation 4x + 9 = 5.
(vi) If 3x + 7 = 1, then the value of 5x + 13 is ………..
(vii) In natural numbers, 4x + 5 = -7 has ……….. solution.
(viii) In integers, 3x – 1 = 4 has …………. solution.
(ix) 5x + ………. = 13 has the solution -3.
(x) If a number is increased by 15, it becomes 50. Then the number is ……..
(xi) If 63 exceed another number by 21, then the other number is …………
(xii) If x ∈ W, then the solution set of x < 2 is ………..

(i) A linear equation in one variable
cannot have more than one solution.
(ii) If five times a number is 50, then the number is 10.
(iii) The number 4 is the solution of the equation 2y – 5 = 3.
⇒ 2y = 3 + 5 = 8
⇒ y = 4
(iv) The equation for the statement ‘5
less than thrice a number x is 7’ is 3x – 5 = 7.

Question 2

State whether the following statements are true (T) or false (F):
(i) We can add (or subtract) the same number of expression to both sides of an equation.
(ii) We can divide both sides of an equation by the same non-zero number.
(iii) 3x – 5 = 2(x + 3) + 7 is a linear equation in one variable.
(iv) The solution of the equation 3(x – 4) = 30 is x = 6.
(v) The solution of the equation 3x – 5 = 2 is x = $\frac { 7 }{ 3 }$
(vi) The solution of a linear equation in one variable is always an integer.
(vii) 4x + 5 < 65 is not an equation.
(viii) 2x + 1 = 7 and 3x – 5 = 4 have the same solution.
(ix) $\frac { 9 }{ 4 }$ is a solution of the equation 5x – 1 = 8.
(x) If 5 is a solution of variable x in the equation $\frac { 5x-7 }{ 2 }$ = y, then the value of y is 18.
(xi) One-fourth of a number added to itself given 10, can be represented as $\frac { x }{ 4 }$ + 10 = x.

(i) We can add (or subtract) the same number of
expression to both sides of an equation. (True)
(ii) We can divide both sides of an equation
by the same non-zero number. (True)
(iii) 3x – 5 = 2(x + 3) + 7
is a linear equation in one variable. (True)
3x – 5 = 2x + 6 + 7
⇒ 3x – 2x = 6 + 7 + 5
⇒ x = 18
(iv) The solution of the equation
3(x – 4) = 30 is x = 6. (False)
Correct:
3(x – 4) = 30
⇒ x – 4 = 10

#### Multiple Choice Question (MCQ)

Question 3

Which of the following is not a linear equation in one variable?
(a) 3x – 1 = 7
(b) 5y – 2 = 3 (y + 2)
(c) 2x – 3 = $\frac { 7 }{ 2 }$
(d) 7p + q = 3

Question 5

x = -1 is a solution of the equation
(a) x – 5 = 6
(b) 2x + 5 = 7
(c) 2(x – 2) + 6 = 0
(d) 3x + 5 = 4

Question 11

If the sum of two consecutive even numbers is 54, then the smaller number is
(a) 25
(b) 26
(c) 27
(d) 28

Let first even integer = 2x
Then second integer = 2x + 2
2x + 2x + 2 = 54
⇒ 4x = 54 – 2
⇒ 4x = 52
⇒ x = 13
Smaller even integer = 2 × 13 = 26 (b)

Question 12.
If the sum of two consecutive odd numbers is 28, then the bigger number is
(a) 19
(b) 17
(c) 15
(d) 13

Let first odd number = x
Then second = x + 2
x + x + 2 = 28
⇒ 2x = 28 – 2 = 26
⇒ x = 13
Bigger odd number = 13 + 2 = 15 (c)

Question-13

If 5 added to thrice an integer is -7, then the integer is
(a) -6
(b) -5
(c) -4
(d) 4

Let integer be x, then 3x + 5 = -7
⇒ 3x = -7 – 5
⇒ 3x = -12
⇒ 3x= -14
⇒ x = -4 (c)

Question-14
If the length of a rectangle is twice its breadth and its perimeter is 120 m, then its length is
(a) 20 m
(b) 30 m
(c) 40 m
(d) 60 m

Let breadth of a rectangle = x
Then length = 2x
Perimeter = 2(x + 2x) = 2 × 3x = 6x
6x = 120
⇒ x = 20
Length = 2x = 20 × 2 = 40 m (c)

Question 15.
If the difference of two complementary angles is 10°, then the smaller angle is
(a) 40°
(b) 50°
(c) 45°
(d) 35°

Let first angle = x
Then its complementary angle = 90° – x
Now x – (90° – x) = 10°
⇒ x – 90° + x = 10°
⇒ 2x = 10° + 90° = 100°
⇒ x = 50°
Second angle = 90° – 50° = 40°
Smaller angle = 40° (a)

Question 16.

If the difference of two supplementary angles is 30°, then the larger angle is
(a) 60°
(b) 75°
(c) 90°
(d) 105°

Let first supplementary angle = x
Then second = 180° – x
x – (180° – x) = 30°
⇒ x – 180° + x = 30°
⇒ 2x = 30° + 180° = 210°
⇒ x = 105°
Larger angle = 105° (d)

Question 17.

If x ∈ W, the solution set of the inequation -2 ≤ x < 3 is
(a) {-2, -1,0, 1, 2}
(b) {-1, 0, 1, 2, 3}
(c) {0, 1, 2, 3}
x ∈ W
Solution set -2 ≤ x < 3 = {-2, -1, 0, 1, 2} (a)

Value Based Questions

Question 1

On his 13th birthday, a boy decided to distribute blankets to the poor people instead of giving a party to his friends. Half of the blankets he distributed in an old age home, three fourths of the remaining in an orphanage and rest 20 were distributed to the roadside beggars. Find the number of blankets he had. What values are being promoted

Higher Order Thinking Skills ( HOTS )

Question 1

Two persons start moving from two points A and B in opposite directions towards each other. One person start moving from A at the speed of 4 km/h and meets the other person coming from B after 6 hours. If the distance between A and B is 42 km, find the speed of the other person.

Distance between A and B = 42 km

Speed of one person = 4 km/h
After 6 hours they meet together
Let speed of other person = x km/h
According to the condition,
4 × 6 + x × 6 = 42
⇒ 24 + 6x = 42
⇒ 6x = 42 – 24 = 18
⇒ x = 3
Speed of other person = 3 km/h

Question 2

There are some benches in the classroom. If 4 students sit on each bench then 3 benches remain empty and if 3 students sit on each bench then 3 students remain standing. Find the number of students in the class.

Let number of benches in a classroom = x
According to the condition,
No. of students = (x – 3) × 4 and x × 3 + 3
(x – 3) × 4 = x × 3 + 3
⇒ 4x – 12 = 3x + 3
⇒ 4x – 3x = 3 + 12
⇒ x = 15
Number of benches = 15
and number of students = 15 × 3 + 3 = 45 + 3 = 48

Question 1.
Solve the following equations :
(i) 2 (x – 5) + 3 (x – 2) = 8 + 7 (x – 4)

………….

(i) 2 (x – 5) + 3 (x – 2) = 8 + 7 (x – 4)
Removing group symbols,
2x – 10 + 3x – 6 = 8 + 7x – 28
⇒ 5x- 16 = 7x – 20
⇒ 5x – 7x = – 20 + 16
(Transposing -16 to R.H.S and 7x to L.H.S)
⇒ -2x = -4

Question 2

A number exceeds its three-fifth by 22. Find the number.

Question 3

When 9 is added to twice a number, the result is 3 more than thrice the number. Find the number.

Let the number be x

Twice a number = 2x
Thrice a number = 3x
According to statement,
9 + 2x = 3 + 3x
⇒ 9 – 3 = 3x – 2x
⇒ 6 = x
⇒ x = 6

Question 4

The ten’s digit of a two digit number is twice the unit’s digit. The sum of the number and its unit’s digit is 66. Find the number.

Let the unit’s digit be x.
Ten’s digit = 2x.
The number =10 × 2x + x = 20x + x
According to statement,
10 × 2x + x + x = 66
⇒ 20x + x + x = 66
⇒ 22x = 66
⇒ x = 3
The number = 20x + x = 20 × 3 + 3 = 60 + 3 = 63

Question 5

A student bought some pens at ₹ 8 each and some pencils at ₹ 1.50 each. If the total number of pens and pencils purchased is 16 and their total cost is ₹ 50, how many pens did he buy?

The total number of pens and pencils purchased = 16
Let the number of pens bought = x
The number of pencils bought = 16 – x
Cost of pens bought = 8x
Cost of pencils bought = 1.50 (16 – x)
According to given condition,
8x + 1.50 (16 – x) = ₹ 50
⇒ 8x + 24 – 1.50x = 50
⇒ 6.50x = 50 – 24

Question 6

Arvind is eight years older than his sister. In three years, he will be twice as old as his sister. How old are they now?

Let the sister’s age = x years
Arvind’s age = (x + 8) years.
In three years, sister’s age = (x + 3) years
In three years, Arvind’s age = (x + 8 + 3) years
According to statement,
x + 8 + 3 = 2(x + 3)
⇒ x + 11 = 2x + 6
⇒ x – 2x = 6 – 11
⇒ -x = -5
⇒ x = 5.
Sister’s age = 5 years
Arvind’s age = 5 + 8 = 13 years.

Question 7

The angles of a triangle are in the ratio 1 : 2 : 3. Find their measure in degrees.

Let the angles of a Δ are x, 2x and 3x.
We know that
Sum of ∠s of a Δ is 180°
x + 2x + 3x = 180°
⇒ 6x = 180°
⇒ x = 30°
∠s of a Δ are
1x = 1 × 30° = 30°,
2x = 2 × 30° = 60°,
and 3x = 3 × 30° = 90°

Question 8.
Solve the following in equations and represent their solution on a number line:

……………

— End of Linear Equations Class-7 ML Aggarwal Solutions  :–