# Simple Linear Equations ICSE Class-6th Concise Selina Maths Solutions Ch-22

## Chapter-22 Simple (Linear) Equations (Including Word Problems)

**Simple Linear Equations ICSE Class-6th** Concise Selina Mathematics Solutions Chapter-22 (Including Word Problems) . We provide step by step Solutions of Exercise / lesson-22 **Simple Linear Equations** (Including Word Problems) for **ICSE Class-6 Concise** Selina Mathematics.

Our Solutions contain all type Questions of Exe-22 A, Exe-22 B, Exe-22 C, Exe-22 D and Revision Exercise to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-6 .

**Simple Linear Equations ICSE Class-6th** Concise Selina Mathematics Solutions Chapter-22 (Including Word Problems)

–: Select Topics :–

### Exercise – 22 A **Simple Linear Equations ** (Including Word Problems) for **ICSE Class-6th** Concise Selina Mathematics Solutions

**Question- 1.**

Solve:

(i) x + 2 = 6

(ii) x + 6 = 2

(iii) y + 8 = 5

(iv) x + 4 = – 3

(v) y + 2 = – 8

(vi) b + 2.5 = 4.2

(vii) p + 4.6 = 8.5

(viii) y + 3.2 = – 6.5

(ix) a + 8.9 = – 12.6

(x)…x +2.^{1}⁄_{3}..= 5……..

**Answer-1**

**(i) x + 2 = 6**

⇒ x = 6 – 2

⇒ x = 4

**(ii) x + 6 = 2**

⇒ x = 2 – 6

⇒ x = – 4

**(iii) y + 8 = 5**

⇒ y = 5 – 8

⇒ x = – 3

**(iv) x + 4 = – 3**

x + 4 = – 3

⇒ x = – 3 – 4

⇒ x = – 7

**(v) y + 2 = – 8**

⇒ y = – 8 – 2

⇒ y = – 10

**(vi) b + 2.5 = 4.2**

⇒ b = 4.2 – 2.5

⇒ b = 1.7

**(vii) p + 4.6 = 8.5**

⇒ p = 8.5 – 4.6

⇒ p = 3.9

**(viii) y + 3.2 = – 6.5**

⇒ y = – 6.5 – 3.2

⇒ y = – 9.7

**(ix) a + 8.9 = – 12.6**

⇒ a = – 12.6 – 8.9

⇒ a = – 21.5

**(x)…x +2. ^{1}⁄_{3}..= 5……..**

**(xi)**

(xii)

(xiii)

(xiv)

(xv)

**Question -2.**

**Answer-2**

**(i) x – 3 = 2**

⇒ x = 2 + 3

⇒ x = 5

**(ii) m – 2 = – 5**

⇒ m = – 5 + 2

⇒ m = – 3

**(iii) m – 2 = – 5**

⇒ m = – 5 + 2

⇒ m = – 3

(iv) a – 2.5 = – 4

⇒ a = – 4 + 2.5

⇒ a = – 1.5

(v)

(vi)

**(vii) p – 5.4 = 2.7**

⇒ p = 2.7 + 5.4

⇒ p = 8.1

**(viii) x – 1.5 = – 4.9**

⇒ x = – 4.9 + 1.5

⇒ x = – 3.4

(ix)

**Question -3.**

Solve:

(i) 3x = 12

(ii) 2y = 9

(iii) 5z = 8.5

(iv) 2.5 m = 7.5

(v) 3.2 p = 16

(vi) 2a = 4.6

**Answer-3**:

**Question- 4.**

Solve:

**Answer-4**:

**Question- 5.**

Solve:

**Answer-5**:

**Selina Concise Mathematics solutions Simple Linear Equations** (Including Word Problems) Exercise – 22 B for **ICSE Class-6th**

**Question- 1.**

Solve:

(i) 2x + 5 = 17

(ii) 3y – 2 = 1

(iii) 5p + 4 = 29

(iv) 4a – 3 = – 27

(v) 2z + 3 = – 19

(vi) 7m – 1 = 20

(vii) 2.4x – 3 = 4.2

(viii) 4m + 9.4 = 5

(ix) 6y + 4 = – 4.4

**Answer-1**:

**Question -2.**

Solve:

**Answer-2**:

**Question- 3.**

Solve:

(i) 8m -2 = – 10

(ii) 4x + 2x = 3 + 5

(iii) 4x – x + 5 = 8

(iv) 6x + 2 = 2x + 10

(v) 18 – (2a – 12) = 8a

(vi) 3x + 5 + 2x + 6 + x = 4x + 21

(vii) 3.5x – 9 – 3 = x + 1

(viii) 8x + 6 + 2x – 4 = 4x + 8

(ix) m + (3m – 6m) = – 8 – 14

(x)…5x – 14 = x – (24 + 4x)……

**Answer-3**:

### Exercise – 22 C ** Simple Linear Equations** (Including Word Problems) **Selina Concise Mathematics solutions for ICSE Class-6**

**Question- 1.**

5 – x = 3

**Answer-1**:

5 – x = 3

⇒ 5 – 3 = x

⇒ x = 2

**Question -2.**

2 – y = 8

**Answer-2**:

2 – y = 8

⇒ 2 – 8 = y

⇒ – 6 = y

⇒ y = – 6

**Question -3.**

8.4 – x = -2

**Answer-3**:

8.4 – x = -2

⇒ 8.4 + 2 = x

⇒ x = 10.4

**Question -4.**

**Answer-4**:

**Question -5.**

**Answer-5**:

**Question- 6.**

**Answer-6**:

**Question -7.**

1.6z = 8

**Answer-7**:

**Question -8.**

3a = – 2.1

**Answer-8**:

**Question -9.**

**Answer-9**:

**Question -10.**

**Answer-10**:

**Question- 11.**

– 5x = 10

**Answer-11**:

**Question -12.**

2.4z = -4.8

**Answer-12**:

**Question- 13.**

2y – 5 = -11

**Answer-13**:

2y – 5 = -11

⇒ 2y = – 11 + 5

⇒ 2y = – 6

⇒ y = –^{6}⁄_{2}

⇒ y = – 3

**Question -14.****Simple Linear Equations ICSE Class-6th Concise **

2x + 4.6 = 8

**Answer-14**:

2x + 4.6 = 8

⇒ 2x = 8 – 4.6

⇒ 2x = 3.4

⇒ x = ^{3.4}⁄_{2}

⇒ x = ^{34}⁄_{2 x 10}

x = ^{17}⁄_{10}

x = 1.7

**Question- 15.**

5y – 3.5 = 10

**Answer-15**:

5y – 3.5 = 10

⇒ 5y = 10 + 3.5

⇒ 5y = 13.5

⇒ y = ^{13.5}⁄_{5}

⇒ y = 2.7

**Question- 16.**

3x + 2 = -2.2

**Answer-16**:

3x + 2 = -2.2

⇒ 3x = – 2.2 – 2

⇒ 3x = – 4.2

⇒ x = -4.2/3

⇒ x = – 1.4

**Question -17.**

**Answer-17**:

^{y}⁄_{2} – 5 = 1

⇒ ^{y}⁄_{2 }×2-5×2=1×2

⇒ y – 10 = 2

⇒ y = 2 + 10

⇒ y = 12

**Question- 18.**

**Answer-18**:

^{z}⁄_{3 }-1=-5

⇒ ^{z}⁄_{3}×3-1×3

=-5×3

⇒ z – 3 = – 15

⇒ z = – 15 + 3

⇒ z = – 12

**Question- 19.**

**Answer-19**:

^{x}⁄_{4}+3.6=-1.1

⇒ ^{x}⁄_{4}=-1.1-3.6

⇒ ^{x}⁄_{4}–4.7

⇒ x = – 4.7 × 4

⇒ x = – 18.8

**Question -20.**

-3y – 2 = 10

**Answer-20**:

-3y – 2 = 10

⇒ – 3y = 10 + 2

⇒ – 3y = 12

⇒ y = ^{12}⁄_{-3}

⇒ y= – 4

**Question- 21.**

4z – 5 = 3 – z

**Answer-21**:

4z – 5 = 3 – z

⇒ 4z + z = 3 + 5

⇒ 5z = 8

⇒ z = ^{8}⁄_{5}

= 1.6

**Question -22.**

7x – 3x + 2 =22

**Answer-22**:

7x – 3x + 2 = 22

⇒ 7x – 3x = 22 – 2

⇒ 4x = 20

⇒ x = ^{20}⁄_{4}

⇒ x = 5

**Question- 23.**

6y + 3 = 2y + 11

**Answer-23**:

6y + 3 = 2y + 11

⇒ 6y – 2y = 11 – 3

⇒ 4y = – 8

⇒ y = ^{8}⁄_{4}

⇒ y = 2

**Question -24.**

3 (x + 5) = 18

**Answer-24**:

3(x + 5) = 18

⇒ 3x + 15 = 18

⇒ 3x = 18 – 15

⇒ 3x = 3

⇒ x = ^{3}⁄_{3}=1

⇒ x = 1

**Question- 25.**

5 (x – 2) – 2 (x + 2) = 3

**Answer-25**:

5(x – 2)- 2(x + 2) = 3

⇒ 5x – 10 – 2x – 2 = 3

⇒ 5x – 2x – 10 – 2 = 3

⇒ 3x – 12 = 3

⇒ 3x = 3 + 12

⇒ x = ^{15}⁄_{3}=5

∴ x = 5

**Question- 26.**

(5x – 3) 4 = 3

**Answer-26**:

(5x – 3) 4 = 3

⇒ 20x – 12 =3

⇒ 20x = 3+12

⇒ 20x = 15

⇒ x = ^{15}⁄_{20}

⇒ x = ^{3}⁄_{4}

**Question- 27.**

3(2x + 1) – 2(x – 5) -5 (5 – 2x) = 16

**Answer-27**:

3(2x + 1) -2(x – 5) -5(5 – 2x) = 16

⇒ 6x + 3 – 2x + 10 – 25 + 10x = 16

⇒ 6x – 2x + 10x + 3 + 10 – 25 = 16

⇒ 16x – 2x + 13 – 25 = 16

⇒ 14x – 12 = 16

⇒ 14x = 16 + 12 = 28

⇒ x = ^{28}⁄_{14}=2

∴ x = 2

### Exercise 22 D **Simple Linear Equations **(Including Word Problems) **ICSE Class-6th** Concise Selina Mathematics

**Question 1.**

A number increased by 17 becomes 54. Find the number.

**Answer-1**:

Let the required number = x

∴ According to the sum:

x + 17 = 54

⇒ x = 54 – 17

⇒ x = 37

Required number = 37

**Question****–****2.**

A number decreased by 8 equals 26, find the number.

**Answer-2**:

Let required number = A

∴ According to the sum:

x – 8 = 26

⇒ A = 26 + 8

⇒ A = 34

∴ Required number = 34

**Question-3.**

One-fourth of a number added to two- seventh of it gives 135; find the number.

**Answer-3**:

Let required number = x

∴ According to the sum,

(LCM of 4, 7 = 28)

⇒ x = 9 × 28 = 252

∴ Required number = 252

**Question -4.**

**Answer-4**:

Let the required number = x

According to the sum,

= 8×20 =160

∴ Required number = 160

**Question- 5.****Simple Linear Equations ICSE Class-6th Concise **

A number is increased by 12 and the new number obtained is multiplied by 5. If the resulting number is 95, find the original number.

**Answer-5**:

Let the original number = x

According to the sum,

(x + 12) × 5 = 95

⇒ 5x + 60 = 95

⇒ 5x = 95 – 60

⇒ 5x = 35

⇒ x = ^{35}⁄_{5}=7

∴ The original number = 7

**Question- 6.**

A number is increased by 26 and the new number obtained is divided by 3. If the resulting number is 18; find the original number.

**Answer-6**:

Let the original number = x

According to the sum,

(x + 26) ÷3 = 18

⇒ x+^{26}⁄_{3}=18

⇒ x + 26 = 18 × 3

⇒ x + 26 = 54

⇒ x = 54 – 26 = 28

**Question- 7.**

The age of a man is 27 years more than the age of his son. If the sum of their ages is 47 years, find the age of the son and his father.

**Answer-7**:

Let the age of son = x years

∴ Age of his father = x + 27

According to the sum:

x + x + 27 = 47

⇒ 2x + 27 = 47

⇒ 2x = 47 – 27 = 20

⇒ x = 202=10

∴ Age of son = 10 years

and age of his father = 10 + 27 = 37 years

**Question -8.**

The difference between the ages of Gopal and his father is 26 years. If the sum of their ages is 56 years, find the ages of Gopal and his father.

**Answer-8**:

Let age of Gopal = x years

∴ Age of his father = (x + 26) years

According to the sum,

x + x + 26 = 56

⇒ 2x + 26 = 56

⇒ 2x = 56 – 26 = 30

⇒ x = ^{30}⁄_{2}=15

∴ Age of Gopal = 15 years

and age of his father = 15 + 26 = 41 years

**Question-9.**

When two consecutive natural numbers are added, the sum is 31; find the numbers.

**Answer-9**:

Let first natural number = x

Then second natural number = x + 1

According to the sum,

x + x + 1 = 31

⇒ 2x + 1 = 31

⇒ 2x = 31 – 1 = 30

⇒ x = ^{30}⁄_{2}=15

∴ First natural number = 15

and second number = 15 + 1 = 16

**Question- 10.**

When three consecutive natural numbers are added, the sum is 66, find the numbers.

**Answer-10**:

Let first natural number = x

Then second natural number = x + 1

and third number = x + 2

According to the sum,

x + x + 1 + x + 2 = 66

⇒ 3x + 3 = 66

⇒ 3x = 66 – 3 = 63

⇒ x = ^{63}⁄_{3}=21

∴ First natural number = 21

second number = 21 + 1 = 22

and third number = 22 + 1 = 23

Hence numbers are 21, 22, 23

**Question -11.**

A natural number decreased by 7 is 12. Find the number.

**Answer-11**:

Let the required number = x

Then x – 7 = 12

⇒ x – 7 + 7 = 12 + 7 (Adding 7 to both sides)

x = 19

∴ Required number = 19

**Question-12.**

One fourth of a number added to one- sixth of itself is 15. Find the number.

**Answer-12**:

Let the required number = x

x= ^{180}⁄_{5}

⇒ x = 36

∴ Required number = 36

**Question -13.****Simple Linear Equations ICSE Class-6th Concise **

A whole number is increased by 7 and the new number so obtained is multiplied by 5; the result is 45. Find the number.

**Answer-13**:

Let the required whole number = x

Then (x + 7) × 5 = 45

= (Dividing by 5)

⇒ x + 7 = 9

⇒ x = 9 – 7

x = 2

∴ Required whole number = 2

**Question- 14.**

The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.

**Answer-14**:

Let age of daughter = x years

Then age of man = (x + 23)

∴ x + (x + 23) = 41

x + x + 23 = 41

⇒ 2x + 23 = 41

⇒ 2x = 41 – 23 = 18

⇒ x = ^{18}⁄_{2}=9

∴ Age of man = x + 23 = 9 + 23 = 32 years

**Question -15.**

The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.

**Answer-15**:

Let age of son = x years

The age of woman = x + 19

∴ x + x + 19 = 37

⇒ 2x + 19 = 37

⇒ 2x = 37 – 19 = 18

⇒ x = ^{18}⁄_{2}=9

∴ Age of son = 9 years

**Question- 16. ****Simple Linear Equations ICSE Class-6th Concise **

Two natural numbers differ by 6 and sum of them is 36. Find the larger number.

**Answer-16**:

∵ Difference between two numbers = 6

and their sum = 36

Let first natural number = x

The second number = x – 6

∴ x + x – 6 = 36

⇒ 2x = 36 + 6 = 42

x = ^{42}⁄_{2}=21

∴ Larger number = 21

**Question -17.**

The difference between two numbers is 15. Taking the smaller number as x; find:

(i) the expression for larger number.

(ii) the larger number, if the sum of these numbers is 71.

**Answer-17**:

Difference of two numbers = 15

Let smaller number = x

∴ Second number = x + 15

∴ Larger number = x + 15

If sum of two numbers = 71

Then x + x + 15 = 71

(i) 2x + 15 = 71

⇒ 2x = 71 – 15 = 56

x = ^{56}⁄_{2}=28

(ii) Larger number = x + 15 = 28 + 15 = 43

**Question -18.**

The difference between two numbers is 23. Taking the larger number as x, find:

(i) the expression for smaller number.

(ii) the smaller number, if the sum of these two numbers is 91.

**Answer-18**:

Difference of two numbers = 23

Let Larger number = x

(i) Then smaller number = x – 23

(ii) ∵ Sum of two numbers = 91

Then x + x – 23 = 91

⇒ 2x – 23 = 91

⇒ 2x = 91 + 23 = 114

⇒ x = ^{114}⁄_{2}=57

∴ Smaller number = x – 23 = 57 – 23 = 34

**Question- 19.**

Find three consecutive integers such that their sum is 78.

**Answer-19**:

Sum of three consecutive numbers = 78

Let first number = x

Then second number = x + 1

and third number = x + 2

Then x + x+1+x + 2 = 78

⇒ 3x + 3 = 78

⇒ 3x = 78 – 3 = 75

⇒ x = ^{75}⁄_{3}=25

∴ First number=25

Second number = 25 + 1 = 26

and third number = 26 + 1 = 27

Then the three required numbers are 25, 26, 27

**Question -20.**

The sum of three consecutive numbers is 54. Taking the middle number as x, find:

(i) expression for the smallest number and the largest number.

(ii) the three numbers.

**Answer-20**:

Sum of three consecutive numbers = 54

Middle number = x

(i) The first number = x – 1

and third number = x + 1

(ii) ∴x + x-1+x+1 = 54

⇒ 3x = 54

⇒ x = ^{54}⁄_{3}=18

∴ First number =18 – 1 = 17

and third number =18 + 1 = 19

∴ Three required numbers are 17, 18,19

### Revision Exercise **Simple Linear Equations **(Including Word Problems) for **ICSE Class-6th** Concise Selina Mathematics Solutions

**Question- 1. **Solve each of the following equations :

**Question -i.**

#### 2x + 3 = 7

**Answer-i**:

2x + 3 = 7

⇒ 2x + 3 – 3 = 7 – 3 …(Subtracting 3 from both sides)

⇒ 2x = 4

⇒ ^{2x}⁄_{2}=^{4}⁄_{2} ….(Dividing by 2)

⇒ x = 2

∴ x = 2

**Question -ii**

2x – 3 = 7

**Answer-ii**:

2x – 3 = 7

⇒ 2x – 3 + 3 = 7 + 3 …(Adding 3 to both sides)

⇒ 2x = 10

⇒ ^{2x}⁄_{2}=^{2x}⁄_{2} ….(Dividing by 2)

⇒ x = 2

∴ x = 5

**Question iii.**

2x ÷ 3 = 7

**Answer-iii**:

2x ÷ 3 = 7

⇒ ^{2x}⁄_{3}=7

⇒ ^{2x}⁄_{3}×3=7×3 …(Multiplying by 3)

⇒ 2x = 21

⇒ ^{2x}⁄_{2}=^{21}⁄_{2} ….(Dividing by 2)

⇒ x = ^{21}⁄_{2}

= ..10.^{1}⁄_{2}………………..

**Question- iv.**

3x – 8 = 13

**Answer-iv**:

3y – 8 = 13

⇒ 3y – 8 + 8 = 13 + 8 …(Adding 8 to both sides)

⇒ 3y = 21

⇒ ^{3y}⁄_{3}=^{21}⁄_{3} ….(Dividing by 3)

∴ y = 7

**Question -v.**

3y + 8 = 13

**Answer-v**:

3y + 8 = 13

⇒ 3y + 8 – 8 = 13 – 8 …(Substracting 8 from both sides)

⇒ 3y = 5

⇒ ^{3y}⁄_{3}=^{5}⁄_{3} ….(Dividing by 3)

∴ y = ^{5}⁄_{3}

⇒ y= .1.^{2}⁄_{3}………

**Question- vi.**

3y ÷ 8 = 13

**Answer-vi**:

3y ÷ 8 = 13

⇒ ^{3y}⁄_{8}=13

⇒ ^{3y}⁄_{8}×8=13×8 …(Multiplying by 8)

⇒ 3y = 104 ….(Dividing by 3)

∴ y = .^{104}⁄_{3}…= 34 ^{2}⁄_{3}………………………………………..

**Question -vii.**

x – 3 = .5 ^{1}⁄_{2}..

**Answer-vii**:

x – 3 = .5 ^{1}⁄_{2}..

⇒ x – 3 + 3 = 5 ^{1}⁄_{2}.+3 ..(Adding 3 to both sides)

∴ x = 8 ^{1}⁄_{2}.

**Question -viii.**

^{3x}⁄_{5}.+4=13

**Answer-viii**:

^{3x}⁄_{5}.+4=13

⇒ ^{3x}⁄_{5}+4-4=13-4 ..(subtracting 4 from both sides)

⇒ ^{3x}⁄_{5}=9

⇒ ^{3x}⁄_{5}×^{5}⁄_{3}=9× ^{5}⁄_{3} …(Multiplying by ^{5}⁄_{3})

∴ x = 15

**Question- ix.**

u + 3 ^{1}⁄_{4}.=4 ^{1}⁄_{3}.

**Answer-9**:

u + 3 ^{1}⁄_{4}.=4 ^{1}⁄_{3}.

⇒u+^{13}⁄_{4}=^{13}⁄_{3}

⇒u+^{13}⁄_{4}–^{13}⁄_{4}=^{13}⁄_{3}–^{13}⁄_{4} …(Substracting ^{13}⁄_{4} from both sides)

⇒u=^{52-39}⁄_{12}= ^{13}⁄_{12}

.⇒….1 ^{1}⁄_{12}

**Question -x.**

5x – 2.4 = 4.9

**Answer-x**:

5x – 2.4 = 4.9

⇒ 5x – 2.4 + 2.4 = 4.9 + 2.4 …(Adding 2.4 to both sides)

⇒ 5x = 7.3

⇒ ^{5x}⁄_{5}=^{7.3}⁄_{5} ..(Dividing by 5)

∴ x = 1.46

**Question- xi.**

5y + 4.9 = 2.4

**Answer-xi**:

5y + 4.9 = 2.4

⇒ 5x + 4.9 – 4.9 = 2.4 – 4.9 …(Substracting 4.9 from both sides)

⇒ 5y = – 2.5

⇒ ^{5y}⁄_{5 }= –^{2.5}⁄_{5} ..(Dividing by 5)

∴ x = – 0.5

**Question- xii.**

48 z + 3.6 = 1.2

**Answer-xii**:

48 z + 3.6 = 1.2

⇒ 4.8z + 3.6 – 3.6 = 1.2 – 3.6 …(Substracting 3.6 from both sides)

⇒ 4.8z = – 2.4

⇒ ^{4.8z}⁄_{4.8}=-^{2.4}⁄_{4.8} ..(Dividing by 4.8)

∴ z = ^{-1}⁄_{2}

= – 0.5

**Question -xiii.****Simple Linear Equations ICSE Class-6th Concise **

^{x}⁄_{2} – 3 = 5

**Answer-xiii**

^{x}⁄_{2} – 3 = 5

⇒ ^{x}⁄_{2}-3+3=5+3 …(Adding 3 to both sides)

⇒ ^{x}⁄_{2}=8

⇒ ^{x}⁄_{2}×2=8×2 ..(Multiplying by 2)

∴ x = 16

**Question- xiv.**

**Answer-xiv**:

^{y}⁄_{3}+7=2

⇒ ^{y}⁄_{3}+7-7=2-7 …(Substracting 7 from both sides)

⇒ ^{y}⁄_{3}=-5

⇒ ^{y}⁄_{3}×3=-5×3 ..(Multiplying by 3)

∴ y = – 15

**Question -xv.**

**Answer-xv**:

(Multiplying both side by ^{3}⁄_{2})

m= 13

**Question- xvi.**

-3x + 4 = 10

**Answer-xvi**:

– 3x + 4 = 10

⇒ – 3x + 4 – 4 = 10 – 4 (Substracting 4 from both sides)

⇒ – 3x = 6

⇒ – ^{3x}⁄_{-3 }=^{6}⁄_{-3} (Dividing by – 3)

∴ x = -2

**Question -xvii.**

5 = x – 3

**Answer-xvii**:

5 = x – 3

⇒ 5 + 3 = x – 3 + 3 (Adding 3 to both sides)

⇒ 8 = x

∴ x = 8

**Question -xviii.**

8y = 3- 3y

**Answer**:**-xviii.**

8y = 3- 3y

⇒ 18 – 3 = 3 – 3y – 3 (Substrating 3 from both sides)

⇒ 15 = – 3y

⇒ ^{15}⁄_{-3}=-^{3y}⁄_{-3} (Dividing by -3)

⇒ – 5 = y

∴ y = – 5

**Question- xix.**

4x = 4.9 = 6.5

**Answer-xix**:

4x + 4.9 = 6.5

⇒ 4x + 4.9 – 4.9 = 6.5 – 4.9

(Substracting 4.9 from both sides)

⇒ 4x = 1.6

⇒ ^{4x}⁄_{4}=^{1.6}⁄_{4} (Dividing by 4)

⇒ x = 0.4

∴ x = 0.4

**Question- xx.**

3z + 2 = -4

**Answer-xx**:

3z + 2 = -4

⇒ 3z + 2 – 2 = – 4 – 2 (Substrating -2 from both sides)

⇒ 3z = – 6

⇒ ^{3z}⁄_{3}=-^{6}⁄_{3} (Dividing by 3)

∴ z = – 2

**Question -xxi.**

7y – 18 = 17

**Answer-xxi**:

7y -18 = 17

⇒ 7y – 18 + 18 = 17 + 18 (Adding 18 to both sides)

⇒ 7y = 35

(Dividing by 7)

∴ y = 5

**Question- xxii.**

^{x}⁄_{1.2} -6=1

**Answer-xxii**:

^{x}⁄_{1.2} -6=1

⇒ ^{x}⁄_{1.2}-6+6=1+6 (Adding 6 to both sides)

⇒ ^{x}⁄_{1.2} = 7

⇒ ^{x}⁄_{1.2}=7×1.2 (Multiplying by 1.2)

∴ x = 8.4

**Question- xxiii.**

^{z}⁄_{2.4}+3.6=5.1

**Answer-xxiii**:

^{z}⁄_{2.4}+3.6=5.1

⇒^{z}⁄_{2.4}+3.6-3.6=5.1-3.6 (Substracting 3.6 from both sides)

⇒ ^{z}⁄_{2.4} = 1.5

⇒ ^{z}⁄_{2.4}×2.4=1.5×2.4 (Multiplying by 2.4)

⇒ z = 3.60

∴ z = 3.6

**Question- xxiv.**

^{y}⁄_{1.8}-2.1=-2.8

**Answer-xxiv**:

^{y}⁄_{1.8}-2.1=-2.8

⇒ ^{y}⁄_{1.8}-2.1+2.1=-2.8+2.1 (Adding 2.1 to both sides)

⇒ ^{y}⁄_{1.8} = – 0.7

⇒ ^{y}⁄_{1.8}×1.8=-0.7×1.8 (Multiplying by 1.8)

∴ y = – 1.26

**Question- xxv.**

7x – 2 = 4x + 7

**Answer-xxv**:

7x – 2 = 4x + 7

⇒ 7x – 2 + 2 = 4x + 7 + 2 ..(Adding 2 to both sides)

⇒ 7x = 4x + 9

⇒ 7x – 4x = 4x + 9 – 4x …(Substracting 4x from both sides)

⇒ 3x = 9

(Dividing by 3)

∴ x = 3

**Question- xxvi.**

3y -(y + 2) = 4

**Answer-xxvii**:

3z – 18 = z – (12 – 4z)

⇒ 3z – 18 = z – 12 + 4z

⇒ 3z – 18 = 5z – 12

⇒ 3z – 18 + 18 = 5z – 12 + 18 …(Adding 18 to both sides)

⇒ 3z = 5z + 6

⇒ 3z – 5z = 5z + 6 – 5z (Subtracting 5z from both sides)

⇒ – 2z = 6

∴ z = – 3

**Question- xxvii.**

3z – 18 = z – (12 – 4z)

**Answer-xxvii.**

3z – 18 = z – (12 – 4z)

⇒ 3z – 18 = z – 12 + 4z

⇒ 3z – 18 = 5z – 12

⇒ 3z – 18 + 18 = 5z – 12 + 18 …(Adding 18 to both sides)

⇒ 3z = 5z + 6

⇒ 3z – 5z = 5z + 6 – 5z (Subtracting 5z from both sides)

⇒ – 2z = 6

…(Dividing by -2)

∴ z = – 3

**Question -xxviii.**

**Answer-xxviii**:

**Question- xxix.**

**Answer-**** xxix.**

**Question- xxx.**

**Answer-xxx**:

**Question- xxxi.**

5x – 2x + 15 = 27

**Answer-xxxi**:

5x – 2x +15 = 27

⇒ 3x + 15 = 27

⇒ 3x + 15 – 15 = 27 – 15 …(Subtracting 15 from both sides)

⇒ 3x = 12

..(Dividing by 3)

⇒ x = 4

**Question- xxxii.**

5y – 15 = 27 -2y

**Answer-xxxii**:

5y – 15 = 27 -2y

⇒ 5y + 2y – 15 = 27 – 2y + 2y (Adding 2y to both sides)

⇒ 7y – 15 = 27

⇒ 7y – 15 + 15 = 27 + 15 …(Adding 15 to both sides)

⇒ 7y = 42

…(Dividing by 7)

⇒ y = 6

**Question- xxxiii.**

7z + 15 = 3z – 13

**Answer-xxxiii**:

7z + 15 = 3z – 13

⇒ 7z + 15 – 3z = 3z – 13 – 3z (Subtracting 3z from both sides)

⇒ 4z + 15 = – 13

⇒ 4z + 15 – 15 = – 13 – 15 …(Subtracting 15 from both sides)

⇒ 4z = – 28

…(Dividing by 4)

⇒ z = – 7

**Question -xxxiv.**

2 (x -3) – 3 (x-4) =12

**Answer-xxxiv**:

2 (x – 3) – 3 (x – 4) =12

⇒ 2x – 6 – 3x + 12 = 12

⇒ – x + 6 = 12

⇒ – x + 6 – 6 = 12 – 6 …(Subtracting 6 from both sides)

⇒ – x = 6

⇒ x = – 6

**Question- xxxv.**

(7y + 8) + 7 = 8

**Answer-xxxv**:

^{7y+8}⁄_{7}= 8

⇒ ^{7y+8}⁄_{7}=8

⇒^{7y+8}⁄_{7}×7=8×7 …(Multiplying by 7)

⇒ 7y + 8 = 56

⇒ 7y + 8 – 8 – 56 – 8 …(Subtracting 8 from both sides)

⇒ 7y = 48

⇒ ^{7y+8}⁄_{7}=^{48}⁄_{7} ..(Dividing by 7)

⇒ y = ^{48}⁄_{7}

⇒ y =…6.^{6}⁄_{7}………….

**Question -xxxvi.**

2(z – 5) +3 (z + 2) -(3 – 5z) = 10

**Answer-xxxvi**:

2(z – 5) +3 (z + 2) – (3 – 5z) =10

⇒ 2z – 10 + 3z + 6 – 3 + 5z = 10

⇒ 10z – 7 = 10

⇒ 10z – 7 + 7 = 10 + 7 …(Adding 7 to both sides)

⇒ 10z = 17

..(Dividing by 10)

⇒ z = .^{17}⁄_{10}

⇒ z = .1^{7}⁄_{10}

**Simple Linear Equations ICSE Class-6th Concise **

**Question -2.**

A natural number decreased by 7 is 12. Find the number.

**Answer-2**:

Let the required number = x

Then x – 7 = 12

⇒ x – 7 + 7 = 12 + 7 (Adding 7 to both sides)

x = 19

∴ Required number = 19

**Question- 3.**

One-fourth of a number added to one-sixth of It is 15. Find the number.

**Answer-3**:

Let the required number = x

⇒ x = 36

∴ Required number = 36

**Question- 4.**

A whole number is increased by 7 and the number so obtained is multiplied by 5; the result is 45. Find the whole number.

**Answer-4**:

Let the required whole number = x

Then (x + 7) × 5 = 45

(Dividing by 5)

⇒ x + 7 = 9

⇒ x = 9 – 7

x = 2

∴ Required whole number = 2

**Question -5.**

The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.

**Answer-5**:

Let age of daughter = x years

Then age of man = (x + 23)

∴ x + (x + 23) = 41

x + x + 23 = 41

⇒ 2x + 23 = 41

⇒ 2x = 41 – 23 = 18

⇒ x = 18/2 =9

∴ Age of man = x + 23 = 9 + 23 = 32 years

**Question -6.**

The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.

**Answer-6**:

Let age of son = x years

The age of woman = x + 19

∴ x + x + 19 = 37

⇒ 2x + 19 = 37

⇒ 2x = 37 – 19 = 18

⇒ x = 18/2=9

∴ Age of son = 9 years

**Question- 7.**

Two natural numbers differ by 6 and their sum is 36. Find the larger number.

**Answer-7**:

∵ Difference between two numbers = 6

and their sum = 36

Let first natural number = x

The second number = x – 6

∴ x + x – 6 = 36

⇒ 2x = 36 + 6 = 42

x = 42/2=21

∴ Larger number = 21

**Question -8.**

The difference between two numbers is 15. Taking the smaller number as x; find :

(i) the expression for the larger number.

(ii) the larger number, if the sum of these numbers is 71.

**Answer-8**:

Difference of two numbers = 15

Let smaller number = x

∴ Second number = x + 15

∴ Larger number = x + 15

If sum of two numbers = 71

Then x + x + 15 = 71

(i) 2x + 15 = 71

⇒ 2x = 71 – 15 = 56

x = 56/2=28

(ii) Larger number = x + 15 = 28 + 15 = 43

**Question -9.**

The difference between two numbers is 23. Taking the larger number as x, find :

(i) the expression for smaller number.

(ii) the smaller number, if the sum of these two numbers is 91.

**Answer-9**:

Difference of two numbers = 23

Let Larger number = x

(i) Then smaller number = x – 23

(ii) ∵ Sum of two numbers = 91

Then x + x – 23 = 91

⇒ 2x – 23 = 91

⇒ 2x = 91 + 23 = 114

⇒ x = 114/2=57

∴ Smaller number = x – 23 = 57 – 23 = 34

**Question- 10.**

Find the three consecutive integers whose sum is 78.

**Answer-10**:

Sum of three consecutive numbers = 78

Let first number = x

Then second number = x + 1

and third number = x + 2

Then x + x+1+x + 2 = 78

⇒ 3x + 3 = 78

⇒ 3x = 78 – 3 = 75

⇒ x = 75/3=25

∴ First number=25

Second number = 25 + 1 = 26

and third number = 26 + 1 = 27

Then the three required numbers are 25, 26, 27

**Question -11.**

The sum of three consecutive numbers is 54. Taking the middle number as x, find :

(i) the expressions for the smallest number and the largest number.

(ii) the three numbers.

**Answer-11**

Sum of three consecutive numbers = 54

Middle number = x

(i) The first number = x – 1

and third number = x + 1

(ii) ∴x + x-1+x+1 = 54

⇒ 3x = 54

⇒ x = 54/3=18

∴ First number =18 – 1 = 17

and third number =18 + 1 = 19

∴ Three required numbers are 17, 18,19

End of **Simple Linear Equations ICSE** Class-6th Solutions :–

Return to **– **Concise Selina Maths Solutions for ICSE Class -6

Thanks