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When you see an algebraic expression like \(3x < 12\), it's important to understand what you're looking at.

• The expression has two sides, separated by the inequality sign \(<\). The left side is \(3x\) and the right side is \(12\).
• Here, \(3x\) means three times the value of the unknown \(x\).

Breaking down an algebraic expression helps you see the components clearly: a variable, coefficients, and constants. This understanding is crucial when solving problems, as it forms the foundation for finding the solution.Another aspect to note is that algebraic expressions can represent a range of possible values for \(x\), unlike equations that typically have a single solution. Keeping this in mind helps contextualize the steps needed to solve the problem.

Inequalities, like equations, have specific properties that guide how they can be manipulated. Remember these key rules to solve inequalities effectively:

• If you add or subtract the same number from both sides, the inequality remains true. Example: If \(x < 4\), then \(x - 1 < 3\).
• Multiplying or dividing both sides by a positive number does not change the inequality sign. That's why, in our example, dividing by \(3\) didn't affect the \(<\) sign.
• However, if you multiply or divide both sides by a negative number, the inequality sign must be flipped. For example, \(x > 2\) becomes \(-x < -2\) if you multiply both sides by \(-1\).

These properties are crucial to solving inequalities. They ensure each step taken maintains the truth of the inequality and guides you to find all possible solutions.

The primary goal in solving inequalities is to isolate the variable, in this case \(x\). Let's see how we can achieve this effectively:- First, ensure all terms involving \(x\) are on one side of the inequality, while any constants are on the opposite side.- In the given problem \(3x < 12\), the coefficient of \(x\) is \(3\). To isolate \(x\), divide every term by \(3\) (the coefficient), which gives \(x < 4\).- Isolation works similarly to solving algebraic equations. The key difference is applying inequality properties, ensuring the inequality sign is accurately adjusted when necessary.Knowing how to isolate \(x\) effectively is a fundamental skill in algebra. It simplifies solving and clearly shows the range of possible solutions for \(x\). Practice makes it easier to spot the quickest path to isolation.