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  • RD Sharma Class 8 Solutions for Maths
  
  # Class 8 RD Sharma Solutions – Chapter 9 Linear Equation In One Variable – Exercise 9.2 | Set 2
  
  ### Question 14. (1-2x)/7 – (2-3x)/8 = 3/2 + x/4
  
  Solution:
  
  (1-2x)/7 – (2-3x)/8 = 3/2 + x/4
  
  First rearrange the equation
  
  (1-2x)/7 – (2-3x)/8 – x/4 = 3/2
  
  By taking LCM for 7, 8 and 4 which is 56
  
  ((1-2x)8 – (2-3x)7 – 14x)/56 = 3/2
  
  (8 – 16x – 14 + 21x – 14x)/56 = 3/2
  
  (-9x – 6)/56 = 3/2
  
  After cross-multiplying
  
  2(-9x-6) = 3(56)
  
  -18x – 12 = 168
  
  -18x = 168+12
  
  -18x = 180
  
  x = 180/-18
  
  x = -10
  
  Now verify the equation by putting x = -10
  
  (1-2x)/7 – (2-3x)/8 = 3/2 + x/4
  
  x = -10
  
  (1-2(-10))/7 – (2-3(-10))/8 = 3/2 + (-10)/4
  
  (1+20)/7 – (2+30)/8 = 3/2 – 5/2
  
  21/7 – 32/8 = 3/2 – 5/2
  
  3 – 4 = -2/2
  
  -1 = -1
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 15. (9x+7)/2 – (x – (x-2)/7) = 36
  
  Solution:
  
  (9x+7)/2 – (x – (x-2)/7) = 36
  
  First simplify the given equation
  
  (9x+7)/2 – (7x-x+2)/7 = 36
  
  (9x+7)/2 – (6x+2)/7 = 36
  
  By taking LCM for 2 and 7 is 14
  
  (7(9x+7) – 2(6x+2))/14 = 36
  
  (63x+49 – 12x – 4)/14 = 36
  
  (51x + 45)/14 = 36
  
  After cross-multiplying
  
  51x + 45 = 36(14)
  
  51x + 45 = 504
  
  51x = 504-45
  
  51x = 459
  
  x = 459/51
  
  x = 9
  
  Now verify the equation by putting x = 9
  
  (9x+7)/2 – (x – (x-2)/7) = 36
  
  (9x+7)/2 – (6x+2)/7 = 36
  
  x = 9
  
  (9(9)+7)/2 – (6(9)+2)/7 = 36
  
  (81+7)/2 – (54+2)/7 = 36
  
  88/2 – 56/7 = 36
  
  44 – 8 = 36
  
  36 = 36
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 16. 0.18(5x – 4) = 0.5x + 0.8
  
  Solution:
  
  0.18(5x – 4) = 0.5x + 0.8
  
  First rearrange the given equation
  
  0.18(5x – 4) – 0.5x = 0.8
  
  0.90x – 0.72 – 0.5x = 0.8
  
  0.90x – 0.5x = 0.8 + 0.72
  
  0.40x = 1.52
  
  x = 1.52/0.40
  
  x = 3.8
  
  Now verify the equation by putting x = 3.8
  
  0.18(5x – 4) = 0.5x + 0.8
  
  x = 3.8
  
  0.18(5(3.8)-4) = 0.5(3.8) + 0.8
  
  0.18(19-4) = 1.9 + 0.8
  
  2.7 = 2.7
  
  Thus L.H.S. = R.H.S.,
  
  Hence, the equation is verified
  
  ### Question 17. 2/3x – 3/2x = 1/12
  
  Solution:
  
  2/3x – 3/2x = 1/12
  
  By taking LCM for 3x and 2x which is 6x
  
  ((2×2) – (3×3))/6x = 1/12
  
  (4-9)/6x = 1/12
  
  -5/6x = 1/12
  
  After cross-multiplying
  
  6x = -60
  
  x = -60/6
  
  x = -10
  
  Now verify the equation by putting x = -10
  
  2/3x – 3/2x = 1/12
  
  x = -10
  
  2/3(-10) – 3/2(-10) = 1/12
  
  -2/30 + 3/20 = 1/12
  
  ((-2×2) + (3×3))/60 = 1/12
  
  (-4+9)/60 = 1/12
  
  5/60 = 1/12
  
  1/12 = 1/12
  
  Thus L.H.S. = R.H.S.,
  
  Hence the equation is verified.
  
  ### Question 18. 4x/9 + 1/3 + 13x/108 = (8x+19)/18
  
  Solution:
  
  4x/9 + 1/3 + 13x/108 = (8x+19)/18
  
  First rearrange the given equation
  
  4x/9 + 13x/108 – (8x+19)/18 = -1/3
  
  By taking LCM for 9, 108 and 18 which is 108
  
  ((4x×12) + 13x×1 – (8x+19)6)/108 = -1/3
  
  (48x + 13x – 48x – 114)/108 = -1/3
  
  (13x – 114)/108 = -1/3
  
  After cross-multiplying
  
  (13x – 114)3 = -108
  
  39x – 342 = -108
  
  39x = -108 + 342
  
  39x = 234
  
  x = 234/39
  
  x = 6
  
  Now verify the equation by putting x = 6
  
  4x/9 + 1/3 + 13x/108 = (8x+19)/18
  
  x = 6
  
  4(6)/9 + 1/3 + 13(6)/108 = (8(6)+19)/18
  
  24/9 + 1/3 + 78/108 = 67/18
  
  8/3 + 1/3 + 13/18 = 67/18
  
  ((8×6) + (1×6) + (13×1))/18 = 67/18
  
  (48 + 6 + 13)/18 = 67/18
  
  67/18 = 67/18
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 19. (45-2x)/15 – (4x+10)/5 = (15-14x)/9
  
  Solution:
  
  (45-2x)/15 – (4x+10)/5 = (15-14x)/9
  
  First rearranging the given equation
  
  (45-2x)/15 – (4x+10)/5 – (15-14x)/9 = 0
  
  By taking LCM for 15, 5 and 9 which is 45
  
  ((45-2x)3 – (4x+10)9 – (15-14x)5)/45 = 0
  
  (135 – 6x – 36x – 90 – 75 + 70x)/45 = 0
  
  (28x – 30)/45 = 0
  
  After cross-multiplying
  
  28x – 30 = 0
  
  28x = 30
  
  x = 30/28
  
  x = 15/14
  
  Now verify the equation by putting x = 15/14
  
  (45-2x)/15 – (4x+10)/5 = (15-14x)/9
  
  x = 15/14
  
  (45-2(15/14))/15 – (4(15/14) + 10)/5 = (15 – 14(15/14))/9
  
  (45- 15/7)/15 – (30/7 + 10)/5 = (15-15)/9
  
  300/105 – 100/35 = 0
  
  (300-300)/105 = 0
  
  0 = 0
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 20. 5(7x + 5)/3 – 23/3 = 13 – (4x-2)/3
  
  Solution:
  
  5(7x+5)/3 – 23/3 = 13 – (4x-2)/3
  
  First rearrange the given equation
  
  (35x + 25)/3 + (4x – 2)/3 = 13 + 23/3
  
  (35x + 25 + 4x – 2)/3 = (39+23)/3
  
  (39x + 23)/3 = 62/3
  
  After cross-multiplying
  
  (39x + 23)3 = 62(3)
  
  39x + 23 = 62
  
  39x = 62 – 23
  
  39x = 39
  
  x = 1
  
  Now verify the equation by putting x = 1
  
  5(7x+5)/3 – 23/3 = 13 – (4x-2)/3
  
  x = 1
  
  (35x + 25)/3 – 23/3 = 13 – (4x-2)/3
  
  (35+25)/3 – 23/3 = 13 – (4-2)/3
  
  60/3 – 23/3 = 13 – 2/3
  
  (60-23)/3 = (39-2)/3
  
  37/3 = 37/3
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 21. (7x-1)/4 – 1/3(2x – (1-x)/2) = 10/3
  
  Solution:
  
  (7x-1)/4 – 1/3(2x – (1-x)/2) = 10/3
  
  when we expand the given equation,
  
  (7x-1)/4 – (4x-1+x)/6 = 10/3
  
  (7x-1)/4 – (5x-1)/6 = 10/3
  
  By taking LCM for 4 and 6 is 24
  
  ((7x-1)6 – (5x-1)4)/24 = 10/3
  
  (42x – 6 – 20x + 4)/24 = 10/3
  
  (22x – 2)/24 = 10/3
  
  After cross-multiplying
  
  22x – 2 = 10(8)
  
  22x – 2 = 80
  
  22x = 80+2
  
  22x = 82
  
  x = 82/22
  
  x = 41/11
  
  Now verify the equation by putting x = 41/11
  
  (7x-1)/4 – 1/3(2x – (1-x)/2) = 10/3
  
  x = 41/11
  
  (7x-1)/4 – (5x-1)/6 = 10/3
  
  (7(41/11)-1)/4 – (5(41/11)-1)/6 = 10/3
  
  (287/11 – 1)/4 – (205/11 – 1)/6 = 10/3
  
  (287-11)/44 – (205-11)/66 = 10/3
  
  276/44 – 194/66 = 10/3
  
  69/11 – 97/33 = 10/3
  
  ((69×3) – (97×1))/33 = 10/3
  
  (207 – 97)/33 = 10/3
  
  110/33 = 10/3
  
  10/3 = 10/3
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 22. 0.5(x-0.4)/0.35 – 0.6(x-2.71)/0.42 = x + 6.1
  
  Solution:
  
  0.5(x-0.4)/0.35 – 0.6(x-2.71)/0.42 = x + 6.1
  
  First simplify the given equation
  
  (0.5/0.35)(x – 0.4) – (0.6/0.42)(x – 2.71) = x + 6.1
  
  (x – 0.4)/0.7 – (x – 2.71)/0.7 = x + 6.1
  
  (x – 0.4 – x + 2.71)/0.7 = x + 6.1
  
  -0.4 + 2.71 = 0.7(x + 6.1)
  
  0.7x = 2.71 – 0.4 – 4.27
  
  = -1.96
  
  x = -1.96/0.7
  
  x = -2.8
  
  Now verify the equation by putting x = 5
  
  0.5(x-0.4)/0.35 – 0.6(x-2.71)/0.42 = x + 6.1
  
  x = -2.8
  
  0.5(-2.8 – 0.4)/0.35 – 0.6(-2.8 – 2.71)/0.42 = -2.8 + 6.1
  
  -1.6/0.35 + 3.306/0.42 = 3.3
  
  -4.571 + 7.871 = 3.3
  
  3.3 = 3.3
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 23. 6.5x + (19.5x – 32.5)/2 = 6.5x + 13 + (13x – 26)/2
  
  Solution:
  
  6.5x + (19.5x – 32.5)/2 = 6.5x + 13 + (13x – 26)/2
  
  First rearrange the equation
  
  6.5x + (19.5x – 32.5)/2 – 6.5x – (13x – 26)/2 = 13
  
  (19.5x – 32.5)/2 – (13x – 26)/2 = 13
  
  (19.5x – 32.5 – 13x + 26)/2 = 13
  
  (6.5x – 6.5)/2 = 13
  
  6.5x – 6.5 = 13×2
  
  6.5x – 6.5 = 26
  
  6.5x = 26+6.5
  
  6.5x = 32.5
  
  x = 32.5/6.5
  
  x = 5
  
  Now verify the equation by putting x = 5
  
  6.5x + (19.5x – 32.5)/2 = 6.5x + 13 + (13x – 26)/2
  
  x= 5
  
  6.5(5) + (19.5(5) – 32.5)/2 = 6.5(5) + 13 + (13(5) – 26)/2
  
  32.5 + (97.5 – 32.5)/2 = 32.5 + 13 + (65 – 26)/2
  
  32.5 + 65/2 = 45.5 + 39/2
  
  (65 + 65)/2 = (91+39)/2
  
  130/2 = 130/2
  
  65 = 65
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 24. (3x – 8) (3x + 2) – (4x – 11) (2x + 1) = (x – 3) (x + 7)
  
  Solution:
  
  (3x – 8) (3x + 2) – (4x – 11) (2x + 1) = (x – 3) (x + 7)
  
  First simplify the given equation
  
  9x2 + 6x – 24x – 16 – 8x2 – 4x + 22x + 11 = x2 + 7x – 3x – 21
  
  9x2 + 6x – 24x – 16 – 8x2 – 4x + 22x + 11 – x2 – 7x + 3x + 21 = 0
  
  9x2 – 8x2 – x2 + 6x – 24x – 4x + 22x – 7x + 3x – 16 + 21 + 11 = 0
  
  -4x + 16 = 0
  
  -4x = -16
  
  x = 4
  
  Now verify the equation by putting x = 4
  
  (3x – 8) (3x + 2) – (4x – 11) (2x + 1) = (x – 3) (x + 7)
  
  x = 4
  
  (3(4) – 8) (3(4) + 2) – (4(4) – 11) (2(4) + 1) = (4 – 3) (4 + 7)
  
  (12-8) (12+2) – (16-11) (8+1) = 1(11)
  
  4 (14) – 5(9) = 11
  
  56 – 45 = 11
  
  11 = 11
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
  ### Question 25. [(2x+3) + (x+5)]2 + [(2x+3) – (x+5)]2 = 10x2 + 92
  
  Solution:
  
  [(2x+3) + (x+5)]- + [(2x+3) – (x+5)]2 = 10x2 + 92
  
  First simplify the given equation
  
  [3x + 8]2 + [x – 2]2 = 10x2 + 92
  
  Now apply the formula (a+b)2
  
  9x2 + 48x + 64 + x2 – 4x + 4 = 10x2 + 92
  
  After rearranging the equation
  
  9x2 – 10x2 + x2 + 48x – 4x = 92 – 64 – 4
  
  44x = 24
  
  x = 24/44
  
  x = 6/11
  
  Now verify the equation by putting x = 6/11
  
  [(2x+3) + (x+5)]2 + [(2x+3) – (x+5)]2 = 10x2 + 92
  
  x = 6/11
  
  [2(6/11) + 3 + (6/11) + 5]2 + [2(6/11) + 3 – (6/11) – 5]2 = 10(6/11)2 + 92
  
  [(12/11 + 3) + (6/11 + 5)]2 + [(12/11 + 3) – (6/11 + 5)]2 = 10(6/11)2 + 92
  
  [(12+33)/11 + (6+55)/11]2 + [(12+33)/11- (6+55)/11]2 = 10(6/11)2 + 92
  
  [(45/11)+ (61/11)]2 + [(45/11) – (61/11)]2 = 360/121 + 92
  
  (106/11)2 + (-16/11)2 = (360 + 11132)/121
  
  11236/121 + 256/121 = 11492/121
  
  11492/121 = 11492/121
  
  Thus, L.H.S. = R.H.S.,
  
  Hence, the equation is verified.
  
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