TOPICS
Exercise - 2.3

Question-1 :-  Solve the equation and check result 3x = 2x + 18 .

Solution :-
  3x = 2x + 18
  3x - 2x = 18
        x = 18
  Verification : 
  L.H.S = 3x = 3 x 18 = 54
  R.H.S = 2x + 18 = 2 x 18 + 18 = 36 + 18 = 54
  L.H.S = R.H.S
    

Question-2 :-  Solve the equation and check result 5t – 3 = 3t – 5 .

Solution :-
  5t – 3 = 3t – 5
  5t - 3t = -5 + 3
       2t = -2
        t = -2/2
        t = -1
  Verification : 
  L.H.S = 5t – 3 = 5 x (-1) - 3 = -5 - 3 = -8
  R.H.S = 3t – 5 = 3 x (-1) - 5 = -3 - 5 = -8
  L.H.S = R.H.S
    

Question-3 :- Solve the equation and check result 5x + 9 = 5 + 3x .

Solution :-
  5x + 9 = 5 + 3x 
  5x - 3x = 5 - 9
       2x = -4
        x = -4/2
        x = -2 
  Verification : 
  L.H.S = 5x + 9 = 5 x (-2) + 9 = -10 + 9 = -1
  R.H.S = 5 + 3x = 5 + 3 x (-2) = 5 - 6 = -1
  L.H.S = R.H.S
    

Question-4 :-  Solve the equation and check result 4z + 3 = 6 + 2z .

Solution :-
  4z + 3 = 6 + 2z
  4z - 2z = 6 - 3
       2z = 3
        z = 3/2
  Verification : 
  L.H.S = 4z + 3 = 4 x 3/2 + 3 = 2 x 3 + 3 = 6 + 3 = 9
  R.H.S = 6 + 2z = 6 + 2 x 3/2 = 6 + 3 = 9
  L.H.S = R.H.S
    

Question-5 :- Solve the equation and check result 2x – 1 = 14 – x .

Solution :-
  2x – 1 = 14 – x
  2x + x = 14 + 1
       3x = 15
        x = 15/3
        x = 5
  Verification : 
  L.H.S = 2x - 1 = 2 x 5 - 1 = 10 - 1 = 9
  R.H.S = 14 - x = 14 - 5 = 9
  L.H.S = R.H.S
    

Question-6 :-  Solve the equation and check result 8x + 4 = 3 (x – 1) + 7 .

Solution :-
  8x + 4 = 3 (x – 1) + 7
  8x + 4 = 3x - 3 + 7
  8x - 3x = 4 - 4
        5x = 0
         x = 0/5
         x = 0
  Verification : 
  L.H.S = 8x + 4 = 8 x 0 + 4 = 0 + 4 = 4
  R.H.S = 3 (x – 1) + 7 = 3 (0 - 1) + 7 = -3 + 7 = 4
  L.H.S = R.H.S
    

Question-7 :-  Solve the equation and check result x = 4/5 (x + 10) .

Solution :-
  x = 4/5 (x + 10)
  x = 4x/5 + 10 x 4/5
  x - 4x/5 = 2 x 4
  (5x - 4x)/5 = 8
  x/5 = 8
    x = 8 x 5
    x = 40
  Verification : 
  L.H.S = x = 40
  R.H.S = 4/5 (x + 10) = 4/5 (40 + 10) = 4/5 x 50 = 4 x 10 = 40
  L.H.S = R.H.S
    

Question-8 :-  Solve the equation and check result 2x/3 + 1 = 7x/15 + 3 .

Solution :-
  2x/3 + 1 = 7x/15 + 3
  2x/3 - 7x/15 = 3 - 1
  (10x - 7x)/15 = 2
  3x/15 = 2
    x/5 = 2
      x = 10
  Verification : 
  L.H.S = 2x/3 + 1 = (2 x 10)/3 + 1 = 20/3 + 1 = (20 + 3)/3 = 23/3 
  R.H.S = 7x/15 + 3 = (7 x 10)/15 + 3 = 70/15 + 3 = 14/3 + 3 = (14 + 9)/3 = 23/3
  L.H.S = R.H.S
    

Question-9 :- Solve the equation and check result 2y + 5/3 = 26/3 – y .

Solution :-
  2y + 5/3 = 26/3 – y 
  2y + y = 26/3 - 5/3
      3y = (26 - 5)/3
      3y = 21/3
      3y = 7
       y = 7/3
  Verification : 
  L.H.S = 2y + 5/3 = (2 x 7/3) + 5/3 = 14/3 + 5/3 = (14 + 5)/3 = 19/3
  R.H.S = 26/3 – y = 26/3 - 7/3 = (26 - 7)/3 = 19/3
  L.H.S = R.H.S
    

Question-10 :-  Solve the equation and check result 3m = 5 m – 8/5 .

Solution :-
  3m = 5m – 8/5
  8/5 = 5m - 3m
  8/5 = 2m
   2m = 8/5
    m = 8/(5 x 2)
    m = 4/5 
  Verification : 
  L.H.S = 3m = 3 x 4/5 = 12/5
  R.H.S = 5m – 8/5 = 5 x 4/5 - 8/5 = 4 - 8/5 = (20 - 8)/5 = 12/5
  L.H.S = R.H.S
    
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