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Understanding how to isolate the variable is a crucial step when working with inequalities. The goal here is to get the variable by itself on one side of the inequality sign, which helps in identifying the set of values that satisfy the inequality. In the exercise given, the first step involves modifying the inequality so that 'y' stands alone. This is achieved by performing the same action to both sides so that the balance of the inequality is maintained. We add 4 to each side, effectively canceling out the -4 next to 'y' on the left side.

This action changes the equation to a form where the variable is isolated: from \(y - 4 > 2\) to \(y > 6\). It's essential to do the same thing to both sides to ensure the solution to the inequality remains correct and accurate.

The process of combining like terms is a fundamental algebraic technique that simplifies expressions and equations. Like terms are terms that contain the same variables raised to the same power. The aim is to combine them to make more straightforward expressions or inequalities.

In our example, \(y - 4 + 4\) involves like terms where numbers are combined, and since -4 and +4 are opposites, they cancel each other out, leaving us with the variable 'y' alone on one side. The same happens on the right side of the inequality: 2 + 4 gets simplified to 6. This step is critical for understanding the core concept and arriving at a simplified version of the inequality, \(y > 6\), which is easier to interpret.

Inequalities represent a range of possible solutions, in contrast to equations that typically have a distinct answer. When depicting an inequality representation, it's crucial to understand that the solution is referring to all the possible values that satisfy the inequality. After isolating the variable to obtain \(y > 6\), the graphical representation would be a number line with an open circle on the number 6 (indicating that 6 itself is not included in the solution set) and an arrow pointing to the right (showing that any number greater than 6 is a solution to the inequality).

Correct representation provides a visual understanding of all the values that 'y' can take. This aids in grasping the concept that an inequality defines a set of values rather than a single value and can be essential for solving real-world problems where conditions are not fixed to one possibility but rather a range of them.