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The distributive property is a fundamental aspect of algebra that helps simplify expressions and solve equations. It's used to eliminate parentheses by multiplying each term inside the parentheses by the factor outside. In the equation provided, you need to apply the distributive property twice. First, distribute the 5 across the terms inside the parentheses \(2x - 1\), producing \(5 \cdot 2x - 5 \cdot 1\). Next, distribute \(-2\) across the terms inside its parentheses, namely \(3x\), resulting in \(-2 \cdot 3x\). This action simplifies the expression from \[5(2x - 1) - 2(3x)\] to \[10x - 5 - 6x\].
This process makes equations easier to manage, reducing complexity and making the next steps, like combining terms, more straightforward.

Combining like terms is crucial for simplifying algebraic expressions. Terms are considered 'like' if they have exactly the same variables raised to the same powers. In our example, we have two terms with the variable \(x\): \(10x\) and \(-6x\).
To combine these, just add their coefficients: \((10 - 6)x\), simplifying our equation from \[10x - 5 - 6x\] to \[4x - 5\].
This simplification condenses the equation and prepares it for solving, allowing you to deal with fewer terms and making the equation more manageable in subsequent steps.

Solving linear equations involves finding the value of the variable that makes the equation true. After combining like terms, our equation becomes \[4x - 5 = 1\]. The goal is to solve for the variable \(x\). This step involves moving towards isolating the variable, which is integral in linear equations.
The equation here tells you that the term \(4x\), after adjustment, should equal a constant. Solving this involves reversing operations through addition or subtraction to simplify further. As you simplify, closely follow the equation’s rule to maintain balance on both sides.

Isolating the variable is the process that ultimately leads to solving the equation. Once you have your terms combined and simplified, as in the equation \[4x - 5 = 1\], you aim to 'isolate' \(x\). This means getting \(x\) by itself on one side of the equation.
In our example, start by adding 5 to both sides to cancel out the \(-5\) next to \(4x\), leading to \[4x = 6\]. The final step is dividing both sides by 4, thus \(rac{4x}{4} = rac{6}{4}\), which simplifies to \(rac{3}{2}\).
Each operation you perform has an opposite that allows you to peel back layers until you isolate the desired term, ensuring the equation represents a solution.