To simplify the given algebraic expression and equation, we'll use several algebraic properties. Let's analyze each step:
1. **Distributive Property of Multiplication over Addition (or Subtraction)**:
The equation starts with 4(x-7). The distributive property allows us to multiply each term inside the parentheses by 4. This gives us:
```
4 * x + 4 * (-7) = 2x - 6
```
2. **Simplification**:
After applying the distributive property, we simplify the terms by performing the multiplication:
```
4x - 28 = 2x - 6
```
3. **Subtraction Property of Equality**:
To solve for x, we need to isolate x on one side of the equation. We'll start by subtracting 2x from both sides of the equation. This property states that if we subtract the same amount from both sides, the equality is still valid:
```
(4x - 2x) - 28 = (2x - 2x) - 6
```
4. **Combining Like Terms**:
After subtracting 2x from both sides, we combine the terms that contain x, and we also simplify the right side (since 2x - 2x is 0):
```
2x - 28 = -6
```
In these first four steps, we've used two main algebraic properties: the distributive property and the subtraction property of equality. After applying these properties, we perform the operations to simplify the terms, which is a standard practice in algebra but not a specific property. Combining like terms is a part of simplification and helps to isolate the variable for solving the equation.