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### Solved Example 1

2x + 1 = 3

### Solution

Write the original equation,
2x + 1 = 3
Subtract 1 from both sides of the equation,
2x + 1 - 1 = 3 - 1
Simplify,
2x = 2
Divide throughout by 2,
(2x)/2 = 2/2
Simplify,
x = 1

### Solved Example 2

4x - 2 = 4

### Solution

Write the original equation
4x - 2 = 4
Add 2 to both sides of the equation,
4x- 2 + 2 = 4 + 2
Simplify,
4x= 6
Divide throughout by 4,
(4x)/4 = 6/4
x = 3/2

### Solved Example 3

2x = 3 - x

### Solution

Write the original equation,
2x = 3 - x
2x + x = 3 - x + x
Simplify,
3x = 3
Divide throughout by 3,
(3x)/3 = 3/3
Simplify,
x = 1

### Solved Example 4

3x + 4 = 5x - 3

### Solution

Write the original equation,
3x + 4 = 5x - 3
Subtract 4 from both sides of the equation,
3x + 4 - 4 = 5x - 3 - 4
Simplify,
3x = 5x - 7
Subtract 5x from both sides of the equation,
3x - 5x = 5x - 7 - 5x
Simplify,
-2x = -7
Divide throughout by -2,
(-2x)/(-2) = (-7)/(-2)
x = 7/2

### Solved Example 5

x/2 + 1 = x/3 + 2

### Solution

Subtract 1 from both sides of the equation,
x/2 + 1 - 1 = x/3 + 2 - 1
Simplify,
x/2 = x/3 + 1
Subtract x/3 from both sides of the equation,
x/2- x/3 = x/3 + 1 - x/3
Simplify,
x/6 = 1
Multiply throughout by 6,
x/6 * 6 = 1 * 6
x = 6