Tìm x

a) x - 3/4 = 1/2 - 7/3
To solve this equation, we need to get rid of the fractions. We can do this by finding a common denominator for the fractions on both sides of the equation. The common denominator for 4 and 3 is 12.
Multiplying both sides of the equation by 12, we get:
12x - 9 = 6 - 28/3
Next, we can simplify the right side of the equation by finding a common denominator for 6 and 28/3. The common denominator is 3.
6 can be written as 6/1, so we have:
12x - 9 = 6/1 - 28/3
Multiplying 6/1 by 3/3, we get 18/3.
12x - 9 = 18/3 - 28/3
Now, we can combine the fractions on the right side of the equation:
12x - 9 = (18 - 28)/3
12x - 9 = -10/3
To isolate x, we can add 9 to both sides of the equation:
12x = -10/3 + 9
To add -10/3 and 9, we need to find a common denominator. The common denominator is 3.
-10/3 can be written as -10/3 * 3/3 = -30/9.
So we have:
12x = -30/9 + 9
Combining the fractions on the right side of the equation, we get:
12x = (-30 + 81)/9
12x = 51/9
To solve for x, we can divide both sides of the equation by 12:
x = (51/9) / 12
Simplifying the right side of the equation, we get:
x = 51/108
The solution to the equation is x = 17/36.

b) 2/3x - 7/3 = 1/4
To solve this equation, we need to get rid of the fractions. We can do this by finding a common denominator for the fractions on both sides of the equation. The common denominator for 3 and 4 is 12.
Multiplying both sides of the equation by 12, we get:
12 * (2/3x) - 12 * (7/3) = 12 * (1/4)
Simplifying, we have:
8x - 28 = 3
To isolate x, we can add 28 to both sides of the equation:
8x = 3 + 28
8x = 31
To solve for x, we can divide both sides of the equation by 8:
x = 31/8
The solution to the equation is x = 31/8.

c) 3x - 7 = x + 3
To solve this equation, we need to isolate x. We can do this by subtracting x from both sides of the equation and adding 7 to both sides:
3x - x - 7 + 7 = x - x + 3 + 7
Simplifying, we have:
2x = 10
To solve for x, we can divide both sides of the equation by 2:
x = 10/2
Simplifying, we get:
x = 5
The solution to the equation is x = 5.

d) x + 14 = 5 - 2x
To solve this equation, we need to isolate x. We can do this by adding 2x to both sides of the equation and subtracting 14 from both sides:
x + 2x + 14 - 14 = 5 - 14 + 2x
Simplifying, we have:
3x = -9 + 2x
To isolate x, we can subtract 2x from both sides of the equation:
3x - 2x = -9 + 2x - 2x
Simplifying, we have:
x = -9
The solution to the equation is x = -9.

e) 2x - 3 = 5x + 6
To solve this equation, we need to isolate x. We can do this by subtracting 2x from both sides of the equation and subtracting 6 from both sides:
2x - 2x - 3 - 6 = 5x - 2x + 6 - 6
Simplifying, we have:
-9 = 3x
To solve for x, we can divide both sides of the equation by 3:
-9/3 = 3x/3
Simplifying, we get:
-3 = x
The solution to the equation is x = -3.

f) 8 - x = x + 11
To solve this equation, we need to isolate x. We can do this by adding x to both sides of the equation and subtracting 8 from both sides:
8 - x + x - 8 = x + x + 11 - 8
Simplifying, we have:
0 = 2x + 3
To isolate x, we can subtract 3 from both sides of the equation:
0 - 3 = 2x + 3 - 3
Simplifying, we have:
-3 = 2x
To solve for x, we can divide both sides of the equation by 2:
-3/2 = 2x/2
Simplifying, we get:
-3/2 = x
The solution to the equation is x = -3/2.

g) 5(x - 2) - 13 = x(3(x + 1)) - 20
To solve this equation, we need to simplify both sides. First, we can distribute the 5 and the x on the right side of the equation:
5x - 10 - 13 = 3x(x + 1) - 20
Simplifying, we have:
5x - 23 = 3x^2 + 3x - 20
Next, we can move all the terms to one side of the equation to set it equal to zero:
3x^2 + 3x - 20 - 5x + 23 = 0
Simplifying, we have:
3x^2 - 2x + 3 = 0
This equation cannot be easily solved by factoring or using the quadratic formula. Therefore, we can conclude that there is no simple solution for x in this equation.

h) 7(x + 1) - 4 = 5(x + 2) - 11
To solve this equation, we need to simplify both sides. First, we can distribute the 7 and the 5 on the right side of the equation:
7x + 7 - 4 = 5x + 10 - 11
Simplifying, we have:
7x + 3 = 5x - 1
Next, we can move all the terms to one side of the equation to set it equal to zero:
7x - 5x + 3 + 1 = 0
Simplifying, we have:
2x + 4 = 0
To isolate x, we can subtract 4 from both sides of the equation:
2x + 4 - 4 = 0 - 4
Simplifying, we have:
2x = -4
To solve for x, we can divide both sides of the equation by 2:
2x/2 = -4/2
Simplifying, we get:
x = -2
The solution to the equation is x = -2.

i) (2x + 3)(x - 1) = 0
To solve this equation, we can set each factor equal to zero and solve for x:
2x + 3 = 0 or x - 1 = 0
For the first equation, subtracting 3 from both sides gives:
2x = -3
Dividing both sides by 2 gives:
x = -3/2
For the second equation, adding 1 to both sides gives:
x = 1
The solutions to the equation are x = -3/2 and x = 1.

k) (2x - 3)(3/4x + 1) = 0
To solve this equation, we can set each factor equal to zero and solve for x:
2x - 3 = 0 or 3/4x + 1 = 0
For the first equation, adding 3 to both sides gives:
2x = 3
Dividing both sides by 2 gives:
x = 3/2
For the second equation, subtracting 1 from both sides gives:
3/4x = -1
Multiplying both sides by 4/3 gives:
x = -4/3
The solutions to the equation are x = 3/2 and x = -4/3.