91Ó°ÊÓ

Inequality notation is a way to express the relationship between two values where one is not necessarily equal to the other. In the given exercise, the inequality is represented as \(6x < 5\). This uses the less than symbol, "\(<\)", which shows us that the value on the left, \(6x\), is less than the value on the right, 5.
Inequalities can also use other symbols:

• \(>\) means greater than.
• \(\leq\) means less than or equal to.
• \(\geq\) means greater than or equal to.
• \(eq\) means not equal to.

These notations help to quickly convey different types of relationships between numbers, allowing for the concise presentation of a range of possible solutions.

A solution set is a collection of all possible values that satisfy a given inequality. In this problem, once we solve the inequality \(6x < 5\), we find that \(x < \frac{5}{6}\). This means that the solution to this inequality includes any value of \(x\) that is less than \(\frac{5}{6}\).
Using set notation, we can represent this solution set as \(\{ x | x < \frac{5}{6} \}\). This notation tells us that \(x\) can be any number less than \(\frac{5}{6}\). It's like a rule that \(x\) must follow.
A solution set is crucial because it provides a complete picture of all values that meet the criteria set by the inequality, allowing us to understand better the range of possible solutions.

Isolating the variable is a key step when solving inequalities or equations. It involves getting the variable on one side of the inequality and everything else on the other side. In our example, we had \(6x < 5\). To solve for \(x\), we needed to get \(x\) all by itself on one side of the inequality.
To do this, we divided both sides of the inequality by 6, the coefficient of \(x\), which simplifies it to \(x < \frac{5}{6}\). This process involves performing the same mathematical operation on both sides of the inequality, which maintains the inequality's balance.
By isolating the variable, we derive a straightforward expression that indicates the range of values \(x\) can take. This makes it much easier to interpret the final solution and understand what \(x\) represents in the context of the inequality.