1) 12 - (x + 20) = 64
Simplify the equation:
- (x + 20) = 64 - 12
- (x + 20) = 52
Remove the negative sign:
x + 20 = -52
Subtract 20 from both sides:
x = -52 - 20
x = -72

2) 124 - x = -16
Subtract 124 from both sides:
- x = -16 - 124
- x = -140
Multiply both sides by -1 to remove the negative sign:
x = 140

3) 4 - x = -27 - (-15)
Simplify the equation:
4 - x = -27 + 15
4 - x = -12
Add x to both sides:
4 = -12 + x
Subtract 12 from both sides:
-8 = x

4) 20 - 5 . (2 - x) = 45
Simplify the equation:
20 - 10 + 5x = 45
10 + 5x = 45
Subtract 10 from both sides:
5x = 35
Divide both sides by 5:
x = 7

5) 2(x + 3) - 48 : 2^3 = 2
Simplify the equation:
2x + 6 - 48 : 8 = 2
2x + 6 - 6 = 2
2x = -4
Divide both sides by 2:
x = -2

6) 200 - (2x + 6) = 4^3
Simplify the equation:
200 - 2x - 6 = 64
194 - 2x = 64
Subtract 194 from both sides:
-2x = -130
Divide both sides by -2:
x = 65

7) 135 - 5(x + 4) = 35
Simplify the equation:
135 - 5x - 20 = 35
115 - 5x = 35
Subtract 115 from both sides:
-5x = -80
Divide both sides by -5:
x = 16

8) 2(x - 51) = 2 . 2^3 +20
Simplify the equation:
2x - 102 = 16 + 20
2x - 102 = 36
Add 102 to both sides:
2x = 138
Divide both sides by 2:
x = 69

9) 15 + (x - 1)^3 = 42
Subtract 15 from both sides:
(x - 1)^3 = 27
Take the cube root of both sides:
x - 1 = 3
Add 1 to both sides:
x = 4

10) (x - 1)^2 = 4
Take the square root of both sides:
x - 1 = 2 or x - 1 = -2
Add 1 to both sides:
x = 3 or x = -1

11) 11 + 5.(x - 1)^2 = 56
Subtract 11 from both sides:
5.(x - 1)^2 = 45
Divide both sides by 5:
(x - 1)^2 = 9
Take the square root of both sides:
x - 1 = 3 or x - 1 = -3
Add 1 to both sides:
x = 4 or x = -2

12) (x^2 -4)(2x + 10) = 0
Set each factor equal to zero:
x^2 - 4 = 0 or 2x + 10 = 0
Solve each equation separately:
x^2 = 4 or 2x = -10
Take the square root of both sides:
x = 2 or x = -2
Divide both sides by 2:
x = 1 or x = -5

13) 7^2x-6 = 49
Take the logarithm of both sides:
2x - 6 = log7(49)
2x - 6 = 2
Add 6 to both sides:
2x = 8
Divide both sides by 2:
x = 4

14) 4^x + 2^2x+1 = 48
Simplify the equation:
2^2x + 2^2x+1 = 48
2^2x + 2^2x * 2 = 48
2^2x + 2^(2x+1) = 48
Let y = 2^x:
y^2 + 2y = 48
Rearrange the equation:
y^2 + 2y - 48 = 0
Factor the quadratic equation:
(y + 8)(y - 6) = 0
Set each factor equal to zero:
y + 8 = 0 or y - 6 = 0
Solve each equation separately:
y = -8 or y = 6
Substitute back y = 2^x:
2^x = -8 or 2^x = 6
There is no solution for 2^x = -8 because 2^x is always positive.
Take the logarithm of both sides for 2^x = 6:
x = log2(6)