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Inequality equations are fundamental in math, forming the basis for understanding how different values relate to each other. Solving inequalities involves finding a range of possible values for variables that make the inequality true. Unlike equations, inequalities do not have just one solution, but rather a whole set of solutions that satisfy the conditions of the inequality.

When handling inequalities, we use similar approaches to those applied in solving equations, such as adding, subtracting, multiplying, or dividing both sides by the same non-zero number. However, an important distinction to be aware of is that when we multiply or divide both sides of an inequality by a negative number, the inequality sign flips. It changes from '<' to '>' or vice versa, according to the rules dealing with inequalities. This aspect is crucial to avoid common mistakes when determining the correct solution set.

The substitution method is a straightforward and efficient tool for determining whether a particular number is a solution to an inequality. It involves replacing the variable in the inequality with the number in question.

For instance, if we have an inequality like \(2x + 4 \leq 3x - 3\), and we want to check if \(x = 5\) is a solution, we substitute 5 for every instance of \(x\) in the inequality. Always remember to maintain the original inequality signs while substituting. Then, we simplify the resulting numerical inequality by performing basic arithmetic operations. This process is a direct and powerful way to verify potential solutions, ensuring that any proposed value for \(x\) meets the constraints set out by the original inequality.

After using substitution to plug in possible solutions, it's critical to evaluate the resulting statement to determine whether the inequality holds true. Inequality evaluation is essentially a reality check: it confirms or refutes the correctness of the proposed solution.

In the given exercise, after simplifying the substituted values, we get \(14 \leq 12\), which is a false statement. Therefore, we can conclude that \(x = 5\) is not a valid solution to the given inequality. Such evaluations strengthen our understanding of how inequalities operate and guide us to the correct solution set. This critical step assists in building logical reasoning skills and the ability to interpret mathematical relationships beyond textbook exercises.