The document RD Sharma Solutions - Chapter 9 - Linear Equation in One Variable (Part - 2), Class 8, Maths Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

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**PAGE NO 9.11:**

**Question 1:**

**Solve each of the following equation and also check your result in each case:**

** = 3x -10**

**ANSWER:**

**= 3x -10**

or 2x + 5 = 9 x âˆ’30

or 9 x âˆ’2x = 5 + 30

or 7x = 35

or x = 35/7

or x = 5

Verification:L.H.S. = = 15/3 = 5

R.H.S. = 15âˆ’10 = 5

âˆ´ L.H.S. = R.H.S. for x = 5.

**PAGE NO 9.11:**

**Question 2:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 2aâˆ’16 = 3aâˆ’9

or 3aâˆ’2a = âˆ’16 + 9

or a = âˆ’7

Verification:

L.H.S. = = -5

R.H.S. = = -5

âˆ´ L.H.S. = R.H.S. for a = âˆ’-7

**PAGE NO 9.11:**

**Question 3:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 77y + 22 = 30yâˆ’25

or 77yâˆ’30y = âˆ’25âˆ’22

or 47y = âˆ’47

or y = âˆ’47/47 = âˆ’1

Verification:L.H.S. =

R.H.S. =

âˆ´ L.H.S. = R.H.S. for y = âˆ’-1

**PAGE NO 9.11:**

**Question 4:**

**Solve each of the following equation and also check your result in each case:**

**x âˆ’2x + 2âˆ’16/3x + 5 = 3âˆ’7/2x **

**ANSWER:**

x âˆ’2x + 2âˆ’16/3x + 5 = 3âˆ’7/2x

or âˆ’38 x + 42 = 18âˆ’21 x

or âˆ’21 x + 38 x = 42âˆ’18

or 17x = 24

or x = 24/17

Check:L.H.S. = 24/17 âˆ’ 2 Ã— 24/17 + 7 âˆ’ 16/3 Ã— 24/17 = âˆ’33/17

R.H.S. = 3âˆ’ 7/2 Ã— 24/17 = âˆ’33/17

âˆ´ L.H.S. = R.H.S. for x = 24/17

**PAGE NO 9.11:**

**Question 5:**

**Solve each of the following equation and also check your result in each case:**

**1/2x + 7x âˆ’6 = 7x + 1/4**

**ANSWER:**

1/2x + 7x âˆ’6 = 7x + 1/4

or 1/2x + 7x âˆ’7x = 1/4 + 6

or x/2 =

or x/2 = 25/4

or x = 25/2

Check:L.H.S. = 12Ã—25/2 + 7Ã—25/2-6 = 35/14

R.H.S. = 7Ã—25/2 + 1/4 = 35/14

âˆ´ L.H.S. = R.H.S. for x = 25/2

**PAGE NO 9.11:**

**Question 6:**

**Solve each of the following equation and also check your result in each case:**

**3/4 x + 4 x = 7/8 + 6 x âˆ’6**

**ANSWER:**

3/4 x + 4 x = 7/8 + 6 x âˆ’6

or 3/4 x âˆ’2x = 7/8âˆ’6

orâˆ’5 x/ 4 = âˆ’41/8

or âˆ’40 x = âˆ’16/4

or x = âˆ’164/âˆ’40 = 41/10

Check:

L.H.S. = 3/4Ã—41/10 + 4Ã—41/10 = 123/40 + 164/10 =

R.H.S. = 7/8 + 6Ã—41/10 - 6 = 7/8 + 246/10 - 6 =

âˆ´ L.H.S. = R.H.S. for x = 41/10

**PAGE NO 9.11:**

**Question 7:**

**Solve each of the following equation and also check your result in each case:**

**7/2 x âˆ’5/2 x = 20/3x + 10**

**ANSWER:**

7/2 x âˆ’5/2 x = 20/3x + 10

or 40 x + 60 = 6 x

or 34 x = âˆ’60

or x = âˆ’60/34

= âˆ’30/17

Check:

L.H.S. = 7/2Ã—âˆ’30/17âˆ’5/2Ã— âˆ’30/17 = âˆ’30/17

R.H.S. = 20/3Ã—âˆ’30/17 + 10 = âˆ’30/17

âˆ´L.H.S. = R.H.S. for x = âˆ’30/17

**PAGE NO 9.11:**

**Question 8:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 18 x + 9 = 14 x âˆ’6

or 18 x âˆ’14 x = âˆ’6âˆ’9

or 4 x = âˆ’15

or x = âˆ’15/4

Check:

L.H.S. =

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = âˆ’15/4

**PAGE NO 9.11:**

**Question 9:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 12a + 5 = 6a + 7

or 6a = 7âˆ’5

or a = 2/6 = 1/3

Check:

L.H.S. = = -1/3 + 11/6 = 9/6 = 3/2

R.H.S. = 1/3 + 7/6 = 9/6 = 3/2

âˆ´ L.H.S. = R.H.S. for a = 1/3

**PAGE NO 9.11:**

**Question 10:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 3x + 3 = 10âˆ’2x

or 5 x = 10âˆ’3

or x = 7/5

Check:

L.H.S. =

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = 7/5

**PAGE NO 9.11:**

**Question 11:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 4 x âˆ’8 = 3x + 6

or x = 14

L.H.S. = = 21/2-13/2 = 8/2 = 4

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = 14

**PAGE NO 9.11:**

**Question 12:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 85 x + 15 = 12x âˆ’36

or 73x = âˆ’51

or x = âˆ’51/73

Check:L.H.S. = = -255/219 - 124292 = -5473

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = âˆ’51/73

**PAGE NO 9.11:**

**Question 13:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 7x âˆ’35 = âˆ’8 x + 40

or 15 x = 75

or x = 75/15 = 5

Check:

L.H.S. =

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = 5

**PAGE NO 9.11:**

**Question 14:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 8âˆ’16 x = 98âˆ’7x

or âˆ’16 x + 7x = 98âˆ’8

or x = âˆ’90/9

= âˆ’10

Check:L.H.S. = = 3-4 = -1

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = âˆ’-10

**PAGE NO 9.11:**

**Question 15:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 51 x + 45 = 504

or 51 x = 504âˆ’45

or x = 459/51 = 9

Thus, x = 9 is the solution of the given equation.

Check:Substituting x = 9 in the given equation, we get:

L.H.S. = = 88/2âˆ’9 + 7/7 = 44âˆ’9 + 1 = 36

R.H.S. = 36

âˆ´ L.H.S. = R.H.S. for x = 9.

**PAGE NO 9.11:**

**Question 16:**

**Solve each of the following equation and also check your result in each case: 0.18(5 x âˆ’ 4) = 0.5 x + 0.8**

**ANSWER:**

0.18(5 x âˆ’4) = 0.5 x + 0.8

or 0.9 x âˆ’0.72 = 0.5 x + 0.8

or 0.9 x âˆ’0.5 x = 0.8 + 0.72

or 0.4 x = 1.52

or x = 1.52/0.4

or x = 3.8

Thus, x = 3.8 is the solution of the given equation.

Check:Substituting x = 3.8 in the given equation, we get:

L.H.S. = 0.18(5Ã—3.8âˆ’4) = 0.18Ã—15 = 2.7

R.H.S. = 0.5Ã—3.8 + 0.8 = 2.7

âˆ´ L.H.S. = R.H.S. for x = 3.8.

**PAGE NO 9.11:**

**Question 17:**

**Solve each of the following equation and also check your result in each case:**

**2/3x âˆ’3/2x = 1/12**

**ANSWER:**

2/3x âˆ’3/2x = 1/12

or 6 x = âˆ’60

or x = âˆ’60/6

or x = âˆ’10

Thus, x = âˆ’10 is the solution of the given equation.

Check:Substituting x = âˆ’10 in the given equation, we get:

L.H.S. =

R.H.S. = 1/12

âˆ´ L.H.S. = R.H.S. for x = âˆ’10.

**PAGE NO 9.11:**

**Question 18:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 61 x + 36 = 6(8 x + 19) [Multiplying both sides by 108]

or 61 x + 36 = 48 x + 114

or 61 x âˆ’48 x = 114âˆ’36

or 13x = 78

or x = 78/13

or x = 6

Thus, x = 6 is the solution of the given equation.

Check:Substituting x = 6 in the given equation, we get:

L.H.S. =

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = 6.

**PAGE NO 9.12:**

**Question 19:**

**Solve each of the following equation and also check your result in each case: **

**ANSWER:**

[Multiplying both sides by 3]

or 45âˆ’42x = 75âˆ’70 x [After cross multiplication]

or 70 x âˆ’42x = 75âˆ’45

or 28 x = 30

or x = 30/28

or x = 15/14

Thus, x = 15/14 is the solution of the given equation.

Check:Substituting x = 15/14 in the given equation, we get:

L.H.S. =

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = 15/14

**PAGE NO 9.12:**

**Question 20:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 39 x + 23 = 62 [Multiplying both sides by 3]

or 39 x = 62âˆ’23

or x = 39/39

or x = 1

Thus, x = 1 is the solution of the given equation.

Check:Substituting x = 1 in the given equation, we get:

L.H.S. =

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = 1.

**PAGE NO 9.12:**

**Question 21:**

**Solve each of the following equation and also check your result in each case:**

**ANSWER:**

or 11 x âˆ’1 = 40 [Multiplying both sides by 12]

or 11 x = 40 + 1

or x = 41/11

Thus, x = 41/11 is the solution of the given equation.

Check:Substituting x = 41/11 in the given equation, we get:

L.H.S. =

R.H.S. = 10/3

âˆ´ L.H.S. = R.H.S. for x = 41/11

**PAGE NO 9.12:**

**Question 22:**

**Solve each of the following equation and also check your result in each case:****= x + 6.1 **

**ANSWER:**

= x + 6.1

or âˆ’0.4 + 2.71 = 0.7x + 4.27

or 0.7x = 2.71âˆ’0.4âˆ’4.27

or x = âˆ’1.96/0.7 = âˆ’2.8

Thus, x = âˆ’2.8 is the solution of the given equation.

Check:

Substituting x = âˆ’2.8 in the given equation, we get:

L.H.S. == âˆ’4.571 + 7.871 = 3.3

R.H.S. = âˆ’2.8 + 6.1 = âˆ’3.3

âˆ´ L.H.S. = R.H.S. for x = âˆ’2.8

**PAGE NO 9.12:**

**Question 23:**

**Solve each of the following equation and also check your result in each case: 6.5 x + **

**ANSWER:**

6.5 x + = 6.5 x + 13 +

or 6.5 x âˆ’6.5 = 26 [After cross multiplication]

or 6.5 x = 26 + 6.5

or x = 32.5/6.5 = 5

Thus, x = 5 is the solution of the given equation.

Check:

Substituting x = 5 in the given equation, we get:

L.H.S. = 6.5Ã—5 +

R.H.S. = 6.5Ã—5 + 13 +

âˆ´ L.H.S. = R.H.S. for x = 5.

**PAGE NO 9.12:**

**Question 24:**

**Solve each of the following equation and also check your result in each case: (3x âˆ’ 8)(3x + 2) âˆ’ (4 x âˆ’ 11)(2x + 1) = ( x âˆ’ 3)( x + 7)**

**ANSWER:**

(3x âˆ’8)(3x + 2)âˆ’(4 x âˆ’11)(2x + 1) = ( x âˆ’3)( x + 7)

or 9 xÂ² + 6 x âˆ’24 x âˆ’16âˆ’8 xÂ²âˆ’4 x + 22x + 11

= xÂ² + 7x âˆ’3x âˆ’21

or xÂ²âˆ’5 = xÂ² + 4 x âˆ’21

or 4 x = âˆ’5 + 21

or x = 16/4 = 4

Thus, x = 4 is the solution of the given equation.

Check:

Substituting x = 4 in the given equation, we get:

L.H.S. = (3Ã—4âˆ’8)(3Ã—4 + 2)âˆ’(4Ã—4âˆ’11)(2Ã—4 + 1) = 4Ã—14âˆ’5Ã—9 = 11

R.H.S. = (4âˆ’3)(4 + 7) = 11

âˆ´ L.H.S. = R.H.S. for x = 4.

**PAGE NO 9.12:**

**Question 25:**

**Solve each of the following equation and also check your result in each case: [(2x + 3) + ( x + 5)] ^{2} + [(2x + 3) âˆ’ ( x + 5)]^{2} = 10 xÂ² + 92**

**ANSWER:**

[(2x + 3) + ( x + 5)]Â² + [(2x + 3)âˆ’( x + 5)]Â²

= 10 xÂ² + 92

or (3x + 8)Â² + ( x âˆ’2)Â²

= 10 xÂ² + 92

or 9 xÂ² + 48 x + 64 + xÂ²âˆ’4 x + 4

= 10 xÂ² + 92 [ (a + b)Â² = aÂ² + bÂ² + 2ab and (aâˆ’b)Â² = aÂ² + bÂ²âˆ’2ab ]

or 10 xÂ²âˆ’10 xÂ² + 44 x = 92âˆ’68

or x = 24/44

or x = 6/11

Thus, x = 6/11 is the solution of the given equation.

Check:

Substituting x = 6/11 in the given equation, we get:

L.H.S. = [(2 Ã— 6/11 + 3) + (6/11 + 5)]^{2} + [(2 Ã— 6/11 + 3)âˆ’(6/11 + 5)]^{2 }

= [(45/11) + (61/11)]^{2} + [(45/11)âˆ’(61/11)]^{2 }

= (106/11)^{2} + (âˆ’16/11)^{2 }

= 11492/121

R.H.S. =

âˆ´ L.H.S. = R.H.S. for x = 6/11