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When you encounter an inequality, envision it as a balancing scale; your goal is to determine which values will keep it balanced. Solving inequalities is similar to solving equations, but with one key difference: when multiplying or dividing by a negative number, the inequality sign flips!

Always start by clearly isolating the variable on one side. As you manipulate the inequality, perform the same operation on both sides to maintain balance. The solution to an inequality isn't just a single number but a range of values that satisfy the condition of the inequality.

For absolute value inequalities like the one from the exercise, recall that the absolute value represents a number's distance from zero on a number line, without considering direction. Therefore, you must consider both the positive and negative scenarios of the variable inside the absolute value, leading to two separate inequalities that capture the full range of potential solutions.

A compound inequality consists of two or more inequalities joined by the word 'and' or 'or'. If 'and' connects them, you're looking for the overlap in the solutions of each inequality, known as the intersection. If 'or' connects them, any number that satisfies at least one of the inequalities is part of the solution set, known as the union.

Intersecting inequalities create a window of values. In the given exercise, you need values of x that satisfy both conditions: being less than 6 and greater than -18. You effectively search for the common ground between two sets, which in this case, form a continuous range on the number line. Always graphically represent the solutions to compound inequalities on a number line for better visualization and understanding of the overlapping intervals.

Isolating the variable in an inequality is a crucial step towards finding its solution. Your objective is to get the variable by itself on one side of the inequality—this allows you to identify the range of values for which the inequality holds true.

In the exercise, isolating x involved two steps. First, you eliminate additional terms (subtracting 2). This simplifies the inequality to where the variable term stands alone on one side. Second, neutralize any coefficients attached to the variable (multiplying by 3). Once done, you're left with a clear condition that x must fulfill.

Remember, in all these manipulations, the inequality's direction is sacred and must maintain integrity unless you're multiplying or dividing by a negative number. This does not happen in the given example, but it's a point worth noting for tackling a broad array of inequality problems.