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The distributive property is a fundamental algebraic concept that helps simplify expressions by removing parentheses. When you have a term outside the parentheses, like \(-2\), you multiply it by each term within the parentheses. This step is crucial because it eliminates the grouping symbols and distributes the multiplication over the group.
In our example, \(-2(3x - 1)\), the distributive property is applied as follows:
- Multiply \(-2\) by \(3x\) to get \(-6x\).
- Then, multiply \(-2\) by \(-1\). Remember, multiplying two negative numbers gives a positive result, so you get \(+2\).

This transforms the original expression into \(-6x + 2\), helping us move towards a simplified equation.

Combining like terms is the next step in simplifying algebraic expressions. Once we've used the distributive property, we often have terms that need to be combined because they describe the same quantities.
Consider our equation post-distribution: \(-6x + 2 - 3\). Here, \(+2\) and \(-3\) are like terms because they are both constant terms (numbers without variables).
- By combining \(+2\) and \(-3\), we simplify the equation to \(-6x - 1\).

Remember, combining like terms involves basic addition or subtraction. It's crucial because it further simplifies the equation, bringing us closer to isolating our variable.

Finally, we need to solve for the variable, \(x\), which means getting \(x\) alone on one side of the equation. This involves a few simple steps:
- Start with the equation \(-6x - 1 = -4\). You want the \(x\) term by itself, so first, add \(1\) to both sides to eliminate the constant term on the left side. This gives \(-6x = -3\).
- The next step is to divide both sides of the equation by \(-6\) to solve for \(x\). So you perform the division \(\frac{-3}{-6}\).

Don't forget to simplify this fraction to get \(x = \frac{1}{2}\). Solving for \(x\) involves these operations to isolate the variable and determine its value.