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## Exercise 7A

**Solve the following equations. Check your result in each case.**

**3x â€“ 5 = 0****Solution:-**The value of the variable which makes the equation a true statement is called the root of the equation.

Now, find the value of x by considering the given equation,

= 3x â€“ 5 = 0

Transposing â€“ 5 to RHS it becomes 5

= 3x = 5

Multiplying both side by (1/3)

= 3x Ã— (1/3) = 5 Ã— (1/3)

= x = (5/3)

By substituting (5/3) in the place of x in given equation, we get

= 3 Ã— (5/3) â€“ 5 = 0

= 5 â€“ 5 = 0

= 0= 0

âˆ´ LHS = RHS

Hence, the result is verified.

**8x â€“ 3 = 9 â€“ 2x****Solution:-**Now, find the value of x by considering the given equation,

=8x â€“ 3 = 9 â€“ 2x

Transposing â€“ 3 to RHS and it becomes 3 and -2x to LHS it becomes 2x

= 8x + 2x = 9 + 3

= 10x = 11

Multiplying both side by (1/10)

= 10x Ã— (1/10) = 12 Ã— (1/10)

= x = (12/10)

= x = (6/5)

By substituting (6/5) in the place of x in given equation, we get

LHS,

= 8 Ã— (6/5) – 3

= (48/5) – 3

= (48-15/5)

= (33/5)

RHS,

= 9 â€“ 2 Ã— (6/5)

= 9 â€“ (12/5)

= (45 â€“ 12)/5

= (33/5)

By comparing LHS and RHS

= (33/5) = (33/5)

âˆ´ LHS = RHS

Hence, the result is verified.

**7 â€“ 5x = 5 â€“ 7x****Solution:-**Now, find the value of x by considering the given equation,

=7 â€“ 5x = 5 â€“ 7x

Transposing 7 to RHS and it becomes -7 and -7x to LHS it becomes 7x

= 7x â€“ 5x = 5 – 7

= 2x = -2

Multiplying both side by (1/3)

= 2x Ã— (1/2) = -2 Ã— (1/2)

= x = (-2/2)

= x = -1

By substituting -1 in the place of x in given equation, we get

LHS,

= 7 â€“ 5 Ã— (-1)

= 7 â€“ (-5)

= 7 + 5

= 12

RHS,

= 5 â€“ 7 Ã— (-1)

= 5 â€“ (-7)

= 5 + 7

= 12

By comparing LHS and RHS

= 12 = 12

âˆ´ LHS = RHS

Hence, the result is verified.

**3 + 2x = 1 â€“ x****Solution:-**Now, find the value of x by considering the given equation,

=3 + 2x = 1 â€“ x

Transposing 3 to RHS and it becomes -3 and -x to LHS it becomes x

= 2x + x = 1 – 3

= 3x = -2

Multiplying both side by (1/3)

= 3x Ã— (1/3) = -2 Ã— (1/3)

= x = (-2/3)

By substituting -2/3 in the place of x in given equation, we get

LHS,

= 3 + 2 Ã— (-2/3)

= 3 + (-4/3)

= 3 – (4/3)

= (9 – 4) / 3

= 5/3

RHS,

= 1 â€“ (-2/3)

= 1 + (2/3)

= (3 + 2)/ 3

= 5/3

By comparing LHS and RHS

= 5/3 = 5/3

âˆ´ LHS = RHS

Hence, the result is verified.

**2 (x â€“ 2) + 3 (4x â€“ 1) = 0****Solution:-**The above question can be written as,

= 2x â€“ 4 + 12x â€“ 3 = 0

Now, find the value of x by considering the above equation,

= 2x + 12x â€“ 4 â€“ 3 = 0

= 14x â€“ 7 = 0

Transposing -7 to RHS and it becomes 7

= 14x = 7

Multiplying both side by (1/14)

= 14x Ã— (1/14) = 7 Ã— (1/14)

= x = (7/14)

= x = 1/2

By substituting 1/2 in the place of x in given equation, we get

LHS,

= (2 Ã— (1/2)) â€“ 4 + (12 Ã— (1/2)) â€“ 3

= 1â€“ 4 + 6 â€“ 3

= 7 â€“ 7

= 0

By comparing LHS and RHS

= 0 = 0

âˆ´ LHS = RHS

Hence, the result is verified.

**5 (2x â€“ 3) – 3 (3x â€“ 7) = 5****Solution:-**The above question can be written as,

= 10x â€“ 15 – 9x + 21 = 5

Now, find the value of x by considering the given equation,

= 10x – 15 â€“ 9x + 21 = 5

= x + 6 = 5

Transposing 6 to RHS and it becomes -6

= x = 5 â€“ 6

= x = -1

By substituting -1 in the place of x in given equation, we get

LHS,

= 10 (-1) -15 -9(-1) + 21

= -10 â€“ 15 + 9 + 21

= -25 + 30

= 5

By comparing LHS and RHS

= 5 = 5

âˆ´ LHS = RHS

Hence, the result is verified.

**2x â€“ (1/3) = (1/5) â€“ x****Solution:-**Now, find the value of x by considering the given equation,

=2x â€“ (1/3) = (1/5) â€“ x

Transposing â€“ (1/3) to RHS and it becomes (1/3) and – x to LHS it becomes x

= 2x + x = (1/5) + (1/3)

= 3x = (3 + 5) / 15

= 3x = 8/15

Multiplying both side by (1/3)

= 3x Ã— (1/3) = (8/15) Ã— (1/3)

= x = (8/45)

By substituting (8/45) in the place of x in given equation, we get

LHS,

= 2 Ã— (8/45) â€“ (1/3)

= (16/45) â€“ (1/3)

= (16 â€“ 15) / 45

= (1/45)

RHS

= (1/5) â€“ (8/45)

= (9-8) / 45

= (1/45)

By comparing LHS and RHS

= (1/45) = (1/45)

âˆ´ LHS = RHS

Hence, the result is verified.

**(1/2)x- 3 = 5 + (1/3)x****Solution:-**Now, find the value of x by considering the given equation,

= (1/2)x- 3 = 5 + (1/3)x

Transposing -3 to RHS and it becomes 3 and (1/3)x to LHS it becomes (-1/3)x

= (1/2)x – (1/3)x = 5 + 3

= ((3-2)/6)x = 8

= (1/6)x = 8

Multiplying both side by 6

= 6 Ã— (1/6)x = 8 Ã— 6

= x = 48

By substituting 48 in the place of x in given equation, we get

LHS,

= (1/2) Ã— (48) – 3

= (48/2) – 3

= 24 – 3

= 21

RHS,

= 5 + (1/3) Ã— (48)

= 5 + (48/3)

= 5 + 16

= 21

By comparing LHS and RHS

= 21 = 21

âˆ´ LHS = RHS

Hence, the result is verified.

**(x/2) + (x/4) = (1/8)****Solution:-**Now, find the value of x by considering the given equation,

= (x/2) + (x/4) = (1/8)

= ((2 + 1) / 4) = (1/8)

= (3/4)x = (1/8)

Multiplying both side by (4/3)

= (3/4)x Ã— (4/3) = (1/8) Ã— (4/3)

= x = (1/6)

By substituting (1/6) in the place of x in given equation, we get

LHS,

= (3/4)x

= (3/4) Ã— (1/6)

= (1/8)

RHS,

= (1/8)

By comparing LHS and RHS

= (1/8) = (1/8)

âˆ´ LHS = RHS

Hence, the result is verified.

**3x + 2(x + 2) = 20 â€“ (2x â€“ 5)****Solution:-**The above question can be written as,

= 3x + 2x + 4 = 20 â€“ 2x + 5

Now, find the value of x by considering the above equation,

= 5x + 4 = 20 â€“ 2x + 5

Transposing 4 to RHS and it becomes -4 and -2x to LHS it becomes 2x

= 5x + 2x = 20 â€“ 4 + 5

= 7x = 25 â€“ 4

= 7x = 21

Multiplying both side by (1/7)

= 7x Ã— (1/7) = 21 Ã— (1/7)

= x = 21/7

= x = 3

By substituting 3 in the place of x in given equation, we get

LHS,

= 5x + 4

= 5 Ã— (3) + 4

= 15 + 4

= 19

RHS,

= 20 â€“ 2x + 5

= 20 â€“ 2 Ã— (3) + 5

= 20 â€“ 6 + 5

= 25 â€“ 6

= 19

By comparing LHS and RHS

= 19 = 19

âˆ´ LHS = RHS

Hence, the result is verified.

**13( y â€“ 4) â€“ 3(y-9) â€“ 5(y + 4) = 0****Solution:-**The above question can be written as,

= 13y â€“ 52 â€“ 3y + 27 â€“ 5y â€“ 20 = 0

Now, find the value of y by considering the above equation,

= 13y â€“ 3y â€“ 5y â€“ 52 + 27 â€“ 20 = 0

= 13y â€“ 8y â€“ 72 + 27 = 0

= 5y â€“ 45 = 0

Transposing -45 to RHS and it becomes 45

= 5y = 45

Multiplying both side by (1/5)

= 5y Ã— (1/5) = 45 Ã— (1/5)

= y = 9

By substituting 9 in the place of y in given equation, we get

LHS,

= 5y â€“ 45

= 5 Ã— (9) â€“ 45

= 45 â€“ 45

= 0

RHS,

= 0

By comparing LHS and RHS

= 0 = 0

âˆ´ LHS = RHS

Hence, the result is verified.

**(2m + 5) / 3 = (3m â€“ 10)****Solution:-**The above question can be written as,

= 3 Ã— [(2m + 5)/ 3] = 3 Ã— (3m -10) â€¦ [Multiplying both side by 3]

= (2m + 5) = 9m â€“ 30

Transposing 2m to RHS and it becomes -2m and -30 to LHS it becomes 30

= 30 + 5 = 9m -2m

= 35 = 7m

Multiplying both side by (1/7),

= 7m Ã— (1/7) = 35 Ã— (1/7)

= m = (35/7)

= m = 5

By substituting 5 in the place of m in given equation, we get

LHS,

= 2m + 5

= 2 Ã— (5) + 5

= 10 + 5

= 15

RHS,

= 9m â€“ 30

= 9 Ã— (5) â€“ 30

= 45 â€“ 30

= 15

By comparing LHS and RHS

= 15 = 15

âˆ´ LHS = RHS

Hence, the result is verified.

**6(3x + 2) â€“ 5(6x â€“ 1) = 3(x â€“ 8) â€“ 5(7x â€“ 6) + 9x****Solution:-**The above question can be written as,

= 18x + 12 â€“ 30x + 5 = 3x â€“ 24 â€“ 35x + 30 + 9x

Now, find the value of x by considering the above equation,

Transposing 12, 5 to RHS and it becomes -12, -5 and -35x, 9x, 3x to LHS it becomes 35x, -9x, -3x

= 18x – 30x + 35x â€“ 9x – 3x = -24 + 30 â€“ 12 – 5

= 53x â€“ 42x = 30 â€“ 41

= 11x = -11

Multiplying both side by (1/11),

= 11x Ã— (1/11) = -11 Ã— (1/11)

= x = (-11/11)

= x = -1

By substituting 5 in the place of x in given equation, we get

LHS,

= 18x + 12 â€“ 30x + 5

= 18 (-1) + 12 â€“ 30 (-1) + 5

= -18 + 12 + 30 + 5

= -18 + 47

= 29

RHS,

= 3x â€“ 24 â€“ 35x + 30 + 9x

= 3 (-1) â€“ 24 â€“ 35 (-1) + 30 + 9 (-1)

= -3 â€“ 24 + 35 + 30 â€“ 9

= -36 + 65

= 29

By comparing LHS and RHS

= 15 = 15

âˆ´ LHS = RHS

Hence, the result is verified.

**t â€“ (2t + 5) â€“ 5(1 â€“ 2t) = 2(3 + 4t) â€“ 3(t -4)****Solution:-**The above question can be written as,

= t â€“ 2t â€“ 5 â€“ 5 + 10t = 6 + 8t â€“ 3t + 12

Now, find the value of t by considering the above equation,

Transposing -5, -5 to RHS and it becomes 5, 5 and 8t, -3t to LHS it becomes -8t, 3t

= t â€“ 2t + 10t â€“ 8t + 3t = 6 + 12 + 5 + 5

= 14t â€“ 10t = 28

= 4t = 28

Multiplying both side by (1/4),

= 4t Ã— (1/4) = 28 Ã— (1/4)

= t = 7

By substituting 7 in the place of t in given equation, we get

LHS,

= t â€“ 2t â€“ 5 â€“ 5 + 10t

= 7 – 2Ã— (7) â€“ 5 â€“ 5 + 10(7)

= 7 â€“ 14 â€“ 5 â€“ 5 + 70

= 77 â€“ 24

= 53

RHS,

= 6 + 8t â€“ 3t + 12

= 6 + 8 Ã— (7) â€“ 3 Ã— (7) + 12

= 6 + 56 â€“ 21 + 12

= 74 â€“ 21

= 53

By comparing LHS and RHS

= 15 = 15

âˆ´ LHS = RHS

Hence, the result is verified.

**(2/3)x = (3/8)x + (7/12)****Solution:-**Find the value of x by considering the above equation,

Transposing (3/8)x to RHS and it becomes -(3/8)x.

= (2/3)x â€“ (3/8)x = (7/12)

= [(16 â€“ 9) / 24]x = (7/12)

= (7/24) x = (7/12)

Multiplying both side by (24/7),

= (7/24)x Ã— (24/7) = (7/12) Ã— (24/7)

= x = 2

By substituting 2 in the place of x in given equation, we get

LHS,

= (2/3)x

= (2/3) Ã— (2)

= (4/3)

RHS,

= (3/8)x + (7/12)

= (3/8) Ã— (2) + (7/12)

= (3/4) + (7/12)

= (9 + 7) / (12)

= (16/12)

= (4/3)

By comparing LHS and RHS

= (4/3) = (4/3)

âˆ´ LHS = RHS

Hence, the result is verified.

**[(3x â€“ 1)/ 5] â€“ (x/7) = 3****Solution:-**The above question can be written as,

= [(7 Ã— (3x -1)) â€“ (5 Ã— (x))/35] = 3

= ((21x â€“ 7) â€“ (5x))/35 = 3

= (21x â€“ 7 â€“ 5x)/35 = 3

= (16x â€“ 7)/35 = 3 â€¦ [Multiplying both side by 35]

= [(16x â€“ 7)/35] Ã— 35 = 3 Ã— 35

= 16x â€“ 7 = 105

= 16x = 105 + 7

= 16x = 112 â€¦ [Multiplying both side by 1/16]

= 16x Ã— (1/16) = 112 Ã— (1/16)

= x = 7

By substituting 7 in the place of x in given equation, we get

LHS,

= (16x â€“ 7)/35

= ((16 Ã— 7) â€“ 7)/35

= (112 â€“ 7)/ 35

= (105/35)

= 3

RHS,

= 3

By comparing LHS and RHS

= (4/3) = (4/3)

âˆ´ LHS = RHS

Hence, the result is verified.

## Exercise 7B

**Twice a number when decreased by 7 gives 45. Find the number.****Solution:-**Let the required number be x.

Then,

= 2x â€“ 7 = 45

Transposing -7 to RHS and it becomes 7.

= 2x = 45 + 7

= 2x = 52

Multiplying both side by (1/2)

= 2x Ã— (1/2) = 52 Ã— (1/2)

= x = 26

âˆ´ the required number is 26

**Thrice a number when increased by 5 gives 44. Find the number.****Solution:-**Let the required number be x.

Then,

= 3x + 5 = 44

Transposing 5 to RHS and it becomes -5.

= 3x = 44 – 5

= 3x = 39

Multiplying both side by (1/3)

= 3x Ã— (1/3) = 39 Ã— (1/3)

= x = 13

âˆ´ the required number is 13

**Four added to twice a number yields (26/5). Find the fraction.****Solution:-**Let the required number be x.

Then,

= 2x + 4 = (26/5)

Transposing 4 to RHS and it becomes -4.

= 2x = (26/5) – 4

= 2x = (26 â€“ 20)/5

= 2x = 6/5

Multiplying both side by (1/2)

= 2x Ã— (1/2) = (6/5) Ã— (1/2)

= x = 3/5

âˆ´ the required number is 3/5

**A number when added to its half gives 72. Find the number.****Solution:-**Let the required number be x.

Then,

= x + (x/2) = 72

= (2x + x)/ 2 = 72

= 3x/2 = 72

Multiplying both side by (2)

= (3x/2) Ã— (2) = 72 Ã— 2

= 3x = 144

Again, multiplying both side by (1/3)

= 3x Ã— (1/3) = 144 Ã— (1/3)

= x = 48

âˆ´ the required number is 48

**A number added to its two-thirds is equal to 55. Find the number.****Solution:-**Let the required number be x.

Then,

= x + (2x/3) = 55

= (3x + 2x)/3 = 55

= 5x/3 = 55

Multiplying both side by (3/5)

= (5x/3) Ã— (3/5) = 55 Ã— (3/5)

= x= 11 Ã— 3

= x = 33

âˆ´ the required number is 33

**A number when multiplied by 4, exceeds itself by 45. Find the number.****Solution:-**Let the required number be x.

Then,

= 4x – x = 45

= 3x = 45

Multiplying both side by (1/3)

= 3x Ã— (1/3) = 45 Ã— (1/3)

= x = 15

âˆ´ the required number is 15

**A number is as much greater than 21 as it is less than 71. Find the number.****Solution:-**Let the required number be x.

Then,

= (x â€“ 21) = (71 â€“x)

Transposing -21 to RHS and it becomes 21 and â€“x to LHS it becomes x.

= x + x = 71 + 21

= 2x = 92

Multiplying both side by (1/2)

= 2x Ã— (1/2) = 92 Ã— (1/2)

= x = 46

âˆ´ the required number is 46

**(2/3) of a number is less than the original number by 20. Find the number.****Solution:-**Let the required number be x.

Then,

= (2x/3) = x â€“ 20

Transposing x to LHS and it becomes â€“x.

= (2x/3) â€“ x = -20

= (2x â€“ 3x)/3 = -20

= -x/3 = -20

Multiplying both side by – 3

= (-x/3) Ã— -3 = -20 Ã— -3

= x = 60

âˆ´ the required number is 60

**A number is (2/5) times another number. If their sum is 70. Find the numbers.****Solution:-**Let the required number be x.

Then,

= x + (2x/5) = 70

= (5x + 2x)/5 = 70

= (7x/5) = 70

Multiplying both side by (5/7)

= (7x/5) Ã— (5/7) = 70 Ã— (5/7)

= x = 50

The other number is (2x/5)

= (2 Ã— 50)/5

= 100/5

= 20

âˆ´the required numbers are 50 and 20

**Two- thirds of a number is greater than one-third of the number by 3. Find the number.****Solution:-**Let the required number be x.

Then,

= (2x/3) = (1x/3) + 3

Transposing (1x/3) to LHS and it becomes â€“ (1x/3)

= (2x/3) â€“ (1x/3) = 3

= (2x â€“ 1x)/ 3 = 3

= (1x/3) = 3

Multiplying both side by (3)

= (1x/3) Ã— 3 = 3 Ã— 3

= x = 9

âˆ´the required numbers are 9

**The fifth part of a number when increased by 5 equals its fourth part decreased by 5. Find the number.****Solution:-**Let the required number be x.

Then,

= (x/5) + 5 = (x/4) â€“ 5

Transposing (x/4) to LHS and it becomes â€“ (x/4) and 5 to RHS it becomes -5

= (x/5) â€“ (x/4) = -5 – 5

= (4x â€“ 5x)/20 = -10

= -x/20 = -10

Multiplying both side by (-20)

= (-x/20) Ã— (-20) = (-10) Ã— (-20)

= x = 200

âˆ´the required numbers are 200

**Find two consecutive natural numbers whose sum is 63.****Solution:-**Let the required two consecutive natural numbers be x and (x + 1)

Then,

= x + (x+1) = 63

= x + x + 1 = 63

= 2x + 1 = 63

Transposing 1 to LHS and it becomes â€“ 1

= 2x = 63 -1

= 2x = 62

Multiplying both side by (1/2)

= 2x Ã— (1/2) = 62 Ã— (1/2)

= x = 31

The other number is (x + 1) = 31 + 1 = 32

âˆ´the required two consecutive natural numbers are 31 and 32

**Find two consecutive positive odd integers whose sum is 76****Solution:-**Let the required two consecutive positive odd integers be x and (x + 2)

Then,

= x + (x+2) = 76

= x + x + 2 = 76

= 2x + 2 = 76

Transposing 2 to LHS and it becomes â€“ 2

= 2x = 76 -2

= 2x = 74

Multiplying both side by (1/2)

= 2x Ã— (1/2) = 74 Ã— (1/2)

= x = 37

The other number is (x + 2) = 37 + 2 = 39

âˆ´the required two consecutive natural numbers are 37 and 39

**Find three consecutive positive even integers whose sum is 90****Solution:-**Let the required three consecutive positive even integers be x, (x + 2) and (x + 4)

Then,

= x + (x+2) + (x+4) = 90

= x + x + 2 + x + 4 = 90

= 3x + 6 = 90

Transposing 6 to LHS and it becomes â€“ 6

= 3x = 90 -6

= 3x = 84

Multiplying both side by (1/3)

= 3x Ã— (1/3) = 90 Ã— (1/3)

= x = 30

The other numbers are (x + 2) = 30 + 2 = 32 and (x + 4) = 30 + 4 = 34

âˆ´the required three consecutive positive even integers are 30, 32 and 34

**Divide 184 into two parts such that one-third of one part may exceed one- seventh of the other part by 8.****Solution:-**Let the two parts be x and (184 â€“ x)

Then,

= (1/3)x – (1/7) (184 â€“ x) = 8

= (1/3)x â€“ (184/7) + (x/7) = 8

Transposing â€“ (184/7) to LHS and it becomes (184/7)

= (1/3) x + (x/7) = 8 + (184/7)

= [(7 + 3)/21]x = (56 +184)/7

= (10/21) x = 240/7

Multiplying both side by (21/10)

= (10/21)x Ã— (21/10) = (240/7) Ã— (21/10)

= x = (240 Ã— 21)/ (7 Ã— 10)

= x = (24 Ã— 3)/ (1 Ã— 1)

= x = 72

**A sum of â‚¹ 500 is in the form of denominations of â‚¹ 5 and â‚¹ 10.if the total number of notes is 90. Find the number of notes of each type.****Solution:-**The total number of notes is 90.

Let the number of â‚¹ 5 note be x

And the number of â‚¹ 10 note be (90 â€“x)

Then,

= 5x + 10(90 â€“ x) = 500

= 5x + 900 -10x = 500

= – 5x + 900 = 500

Transposing â€“ 5x to RHS and it becomes 5x and 500 to LHS it becomes -500

= 900 â€“ 500 = 5x

= 400 = 5x

Multiplying both side by (1/5)

= 400 Ã— (1/5) = 5x Ã— (1/5)

= 80 = x

âˆ´the number of â‚¹ 10 note be (90 â€“x) = (90 â€“ 80) = 10 notes

**Sumitra has â‚¹ 34 in 50-paise and 25-paise coins. If the number of 25-paise coins is twice the number of 50-paise coins, how many coins of each kind does she have?****Solution:-**From the question,

Sumitra has â‚¹34 = 3400 paise

Let 50 paise coins be x

And 25 paise coins be 2x

Then,

= 50x + 25 (2x) = 3400

= 50x + 50x = 3400

= 100x = 3400

Multiplying both side by (1/100).

= 100x Ã— (1/100) = (3400) Ã— (1/100)

= x = 34

âˆ´The number of 50 paise coins is 34

The number of 25 paise coins is 2x = 2 Ã— 34 = 68

## Exercise 7c

**Mark against the correct answer in each of the following:**

**If 5x â€“ (3/4) = 2x â€“ (2/3), then x =?****(a)(1/12) (b)(1/4) (C) 36 (d) (1/36)****Solution:-**(d) (1/36)

Because,

Transposing â€“ (3/4) to RHS and it becomes (3/4) and 2x to LHS it becomes -2x

= 5x â€“ 2x = – (2/3) + (3/4)

= 3x = (-8+9)/12

= 3x = 1/12

Multiplying both side by (1/3).

= 3x Ã— (1/3) = (1/12) Ã— (1/3)

= x = 1/36

**If 2z + (8/3) = (1/4) z + 5, then z =?****(a)3 (b)3 (c)(2/5) (d)(4/3)****Solution:-**(d)(4/3)

Because,

Transposing (8/3) to RHS and it becomes – (8/3) and (1/4)z to LHS it becomes â€“(1/4)z

= 2z â€“ (1/4)z = 5 â€“ (8/3)

= [(8-1)/4]z = (15-8)/3

= (7/4)z = 7/3

Multiplying both side by (4/7).

= (7/4)z Ã— (4/7) = ((7/3) Ã— (4/7)

= x = 4/3

**If (2n + 5) = 3(3n â€“ 10), then z =?****(a)5 (b)3 (c)(2/5) (d)(2/5)****Solution:-**(a)5

Because,

= 2n + 5 = 9n â€“ 30

Transposing 2n to RHS and it becomes â€“ 2n and -30 to LHS it becomes 30

= 30 + 5 = 9n -2n

= 35 = 7n

Multiplying both side by (1/7).

= 35 Ã— (1/7) = 7n Ã— (1/7)

= 5 = n

**If (x-1) / (x +1) = (7/9), then x =?****(a)6 (b)7 (c)8 (d)10****Solution:-**(c)8

Because,

= (x-1) / (x +1) = (7/9)

By cross multiplication,

= 9 Ã— (x-1) = 7 Ã— (x +1)

= 9x -9 = 7x + 7

= 9x -7x = 9 + 7

= 2x = 16

= x = (16/2)

= x = 8

- If 8(2x â€“ 5) â€“ 6 (3x â€“ 7) = 1, then x =?(a)2 (b)3 (c)1/2 (d)(1/3)
Solution:-

(c)1/2

Because,

= 8(2x â€“ 5) â€“ 6 (3x â€“ 7) = 1

= 16x -40 â€“ 18x + 42 = 1

= -2x +2 = 1

= 2-1 = 2x

= 1 = 2x

= x = (1/2)

**If (x/2)-1 = (x/3) +4, then x=?****(a)8 (b)16 (c)24 (d)30****Solution:-**(d)30

Because,

= (x/2)-1 = (x/3) +4

= (x/2) â€“ (x/3) = 4 +1

= (3x-2x)/6 = 5

= x/6 =5

= x = 30

**If (2x-1)/3 = ((x-2)/3) + 1, then x =?****(a)2 (b)4 (c)6 (d)8****Solution:-**(a)2

Because,

= (2x-1)/3 = ((x-2)/3) + 1

= [(2x-1)/3)] â€“ [(x-2)/3)] = 1

= [(2x -1) â€“ (x -2)] / 3 = 1

= (2x â€“ 1 â€“ x +2)/ 3 = 1

= x +1 = 3

= x = 3-1

= x = 2

**The sum of two consecutive whole numbers is 53. The smaller number is****(a)25 (b)26 (c)29 (d)23****Solution:-**(b)26

Because,

Let the two consecutive whole numbers be x and (x +1)

= x + (x+1) = 53

= x + x + 1 = 53

= 2x + 1 = 53

= 2x = 53 â€“ 1

= 2x = 52

= x = 52/2

= x = 26

**The sum of two consecutive even number is 86. The larger of two is****(a)46 (b)36 (c)38 (d)44**Solution:-

(d)44

Because,

Let the two consecutive even numbers be x and (x +2)

= x + (x+2) = 86

= x + x + 2 = 86

= 2x + 2 = 86

= 2x = 86 – 2

= 2x = 84

= x = 84/2

= x = 42

The larger number is (x +1) = 42 +2 = 44

## RS Aggarwal Solutions for Class 7 Maths Chapter 7 – Linear Equations in One Variables

Chapter 7 – Linear Equations in One Variables contains 3 exercises and the RS Aggarwal Solutions available on this page provide solutions to the questions present in the exercises. Now, let us have a look at some of the essential concepts discussed in this chapter.

- Linear Equations
- Problems Based on Linear Equations

### Chapter Brief of RS Aggarwal Solutions for Class 7 Maths Chapter 7 – Linear Equations in One Variables

RS Aggarwal Solutions for Class 7 Maths Chapter 7 – Linear Equations in One Variable. In this chapter, we study the meaning of an equation and also that of a linear equation. Meanwhile, also discuss the purpose of the solutions of a linear equation and two methods of obtaining it, One by trial-and-error and another by a systematic method involving addition, subtraction, multiplication or division of some non-zero number on both sides of the equation.At the end of the chapter, we study the formulation and solution of equations for some real-life problems.