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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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