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Inequalities are similar to equations, but instead of two sides being equal, one side is greater or less than the other. To solve inequalities, we aim to isolate the variable just like we do in equations. However, there is one key difference: when multiplying or dividing both sides by a negative number, we must flip the inequality sign. This is an important rule that you should always remember.

In our exercise, we started with the inequality \(4x < 4\). To isolate \(x\), we divided both sides by 4. This operation did not involve a negative number, so we simply simplified the expression to \(x < 1\).

Once you have simplified the inequality, you can plot the solution on a number line. For \(x < 1\), the solution includes all numbers less than 1, making it an open interval on the left side of 1.

Understanding basic prealgebra concepts is crucial for solving problems involving inequalities. These foundational skills include recognizing arithmetic operations, understanding real numbers, and being able to simplify expressions.

Knowing properties such as the distributive property and being able to factor or expand expressions will also come in handy. Moreover, understanding the difference between integers, whole numbers, and rational numbers adds depth to your ability to solve various types of algebraic inequalities.

In the given exercise, simple division is used - one of the four fundamental operations - to solve the inequality. The ability to perform such operations correctly is a core prealgebra skill that underpins many more advanced mathematical concepts.

Mathematical reasoning helps us validate whether or not our solution is correct. It involves evaluating the logic and consistency of our problem-solving process. To check our solution \(x < 1\), we selected a number less than 1, such as 0, and substituted it back into the original inequality.

This step is crucial because it confirms the accuracy of the solution. When we put \(x = 0\) into the inequality \(4x < 4\), we get \(0 < 4\), which is true. This confirms that the logic we followed to arrive at \(x < 1\) is sound.

Developing strong mathematical reasoning skills allows students to approach complex problems with confidence. By routinely checking solutions, students learn to avoid common pitfalls and ensure that their answers are correct, thereby enhancing their overall mathematical proficiency.