Explanation:
For Q1.
1. x + 5 = 8
x = 8 - 5
x = 3
2. -3x + 7 = 16
-3x = 16 - 7
-3x = 9
x = 9/-3
x = -3
3. 3P/7 = 6
3P = 6*7
3P = 42
P = 42/3
P = 14
4. 2(x + 5) = 24
2x + 10 = 24
2x = 24 - 10
x = 14/2
x = 7
5. x/5 - 8 = 9
x/5 = 9 - 8
x = 5
For Q.2:
1. 12 + 4(x + 3(x + 4)) = 108
12 + 4(x + 3x + 12) = 108
12 + 4x + 12x + 48 = 108
60 + 16x = 108
6x = 108 - 60
x = 48/6
x = 8
2. 5x + 7(4 - (x + 3)) = 31
5x + 28 - x + 3 = 31
6x + 31 = 31
6x = 0
x = 0
3. 2(3y - 2(y + 5) + 3) = -4
2(3y - 2y + 10 + 3) = -4
2(y + 13) = -4
2y + 26 = -4
2y = 30
y = 15
4. 20 - 2(2x -(2 - x) + 10) = -44
20 - 2(2x - 2 + x + 10) = -44
20 - 2(3x + 8) = -44
20 - 6x - 16 = -44
4 - 6x = -44
-6x = -44 - 4
-6x = -48
x = -48/-6
x = 8
5. 5(3x - 4(x + 2) + 5(2x + 1)) = 60
5(3x - 4x - 8 + 10x + 5) = 60
5(3x - 4x + 10x - 8 + 5) = 60
5(9x - 3) = 60
45x -15 = 60
45x = 60 + 15
x = 75/45
x = 1.67
For Q.3:
1. x/2 + x/3 = 10
(3x + 2x)/6 = 10
5x/6 = 10
5x = 60
x = 12
2. 1/3(2x/7 - 1) = 3
1/3(2x - 7/7) = 3
2x - 7/7 = 3/(1/3)
2x - 7/7 = 1
2x - 7 = 7
2x = 14
x = 7
3. (P + 2/2) + ( 2P - 6/4) = 5
(2P + 4 + 2P - 6)/4 = 5
(4P - 2)/4 = 5
4P - 2 = 20
4P = 22
P = 5.5
4. x/3 - (2x + 1)/3 - (x - 3)/5
(x - 2x + 1)/3 - (x - 3)/5
(1 - x)/3 - (x - 3)/5
(5 - 5x - 3x - 9)/15
(-8x - 4)/15
5. (y - 2)/3 + (2y + 5)/5 - (y + 7)/3
5/3 + (2y + 5)/5
(25 + 6y + 15)/15
(40 + 6y)/15