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When it comes to understanding inequalities and their solutions, a graph is an invaluable tool. In graphing an inequality, one typically starts with a number line which represents all possible values that the variable can take. For linear inequalities, where there is only one variable involved, the graph is a simple one-dimensional number line.

For the given exercise, the inequality simplified down to a constant, which indicates that every value of x is a solution. This situation is visualized by shading the entire number line, thus showing that every real number is included in the solution set. Normally, if we had a variable remaining after simplification, we would use open or closed circles to indicate whether a number is included or not, and then shade in the direction that represents the set of solutions. The complete shading, as in this case, represents a unique situation where the inequality holds true regardless of the variable's value.

In solving inequalities, one often encounters expressions that can be simplified using the distributive property. This property states that for any real numbers a, b, and c, the equation a(b + c) is equivalent to ab + ac. Essentially, you're distributing the multiplication of a over the addition within the parentheses.

In our exercise, we applied the distributive property in the first step. We took the -6 and multiplied it by each term within the parentheses: \( -6(2x - 10) = -12x + 60 \). This step is critical for simplifying the inequality so that like terms can be combined in subsequent steps. Without properly using the distributive property, we may not accurately simplify an expression, which can lead to incorrect solutions.

Simplifying expressions is a fundamental skill in solving inequalities and equations. It involves reducing an expression to its simplest form by combining like terms and performing basic arithmetic operations. Like terms are terms that have exactly the same variable components, such as \(2x\) and \(3x\), which can be combined to \(5x\).

In our exercise, combining like terms was the key to simplification. We observed that the terms \( -12x \) and \( +12x \) are like terms but since they are additive inverses of each other, they canceled out. This left us with the constant 60. Such a simplification often leads to easier interpretation of the inequality, but in this rare case, it showed that the inequality does not depend on x at all, as all real numbers are part of the solution. This step underlines the importance of carefully simplifying expressions to accurately solve and understand inequalities.