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In algebra, solving inequalities is much like solving equations, with a few exceptions. While equations aim to find a precise value for the variable, inequalities describe a range of possible values. This concept can be especially useful in scenarios where an exact number doesn’t need to be pinpointed, such as budgeting or planning resources. In this exercise, the inequality is solved step by step using basic algebraic manipulations. The primary processes include distribution, collecting like terms, and isolating the variable. Understanding these steps is key as they are applicable to a variety of algebraic expressions and are fundamental for solving any inequality.

A number line is a visual representation that helps in understanding and solving inequalities. It is a straight line on which numbers are arranged at intervals. On this line, each point corresponds to a number, and the solution to an inequality is often represented as a segment or ray on the line.
The number line allows us to easily see which numbers fall into our solution set. For an inequality like \(x \leq 12\), the number \(12\) is marked with a closed circle. This indicates \(12\) is included in the solution. All numbers extending to the left are part of the solution set. This graphical representation helps in quickly grasping the range of solutions.

Finding a mathematical solution to an inequality involves several crucial steps. The solution process uses properties of inequalities: addition or subtraction of the same number from both sides, and multiplication or division by positive numbers while maintaining the inequality's direction.
In our specific example, simplifying the expression is the starting point: distributing, combining like terms, and isolating the variable are essential tasks. Simplifying transforms our original complex inequality into a simpler form, which can be easily managed. Never forget the rule that multiplying or dividing an inequality by a negative number will reverse the direction of the inequality symbol.

Solving inequalities is about finding all possible values of the variable that make the inequality true. It often involves similar steps to solving equations, albeit with additional considerations. In this problem, distributing numbers, combining terms, and isolating the variable are standard steps. But unlike equations, solutions to inequalities describe a set of values rather than a single solution.

• Start by simplifying both sides of the inequality.
• Rearrange the terms to isolate the variable term.
• Perform operations to simplify the inequality further.
• Remember the inequality direction flips when multiplying or dividing by a negative number.

Mastering these steps is important in algebra, as inequalities appear across various topics, providing a foundational skill for advanced mathematics.