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When it comes to understanding the basics of algebra, comprehending algebraic equations is crucial. An algebraic equation is like a balance scale, where the goal is to find the value of the unknown, often represented by a variable, such as 'x' or 'y', that makes the equation true.

In the context of the exercise, we are looking at an equation where the goal is to solve for 'x'. The equation is presented with numbers and variables intermingled, and our job is to perform operations that simplify this equation to a point where the value of 'x' becomes apparent. The first step is to deal with the brackets and to make sure that all terms are properly expanded to reveal the purest form of the equation. It's like unraveling a knot to lay out the string straight.

Moving a step further, we encounter the process of combining like terms. This is a technique used to simplify an algebraic equation by adding or subtracting terms that are similar—meaning they have the same variable raised to the same power.

For example, if we have terms that include 'x', we group them together. In the given equation, we have '0.5x' on one side and '0.3x' on the other. These are like terms because both contain the variable 'x'. By combining these like terms, we consolidate the variables on one side, which simplifies the equation and brings us closer to isolating the variable. It's a bit like gathering apples from different baskets into one, to easily count how many apples we have in total.

The final and most crucial step in solving an algebraic equation is to isolate the variable. This means we want to get the variable we're solving for (in this case, 'x') by itself on one side of the equation, with all other numbers on the opposite side.

To achieve this, we perform inverse operations. For instance, if 'x' is being added to a number, we would subtract that number from both sides of the equation. Conversely, if a number is multiplied by 'x', we would divide both sides of the equation by that number. This step-by-step dance of operations leads us to a point where the variable stands alone, clear and solved. It's like peeling off all the layers to reveal a hidden object.