Final answer:
The notation [x]<3 represents an inequality, usually involving comparisons of numbers, although the brackets typically denote the greatest integer function. Inequalities without brackets, like 'x < 3', show that the value of x must be less than 3.
Step-by-step explanation:
Yes, the notation [x]<3 is an inequality, a mathematical statement which uses inequality symbols to compare values and show how they are related. However, there may be a misunderstanding with the use of brackets, as typically the use of brackets [] would indicate the greatest integer function, also known as the floor function.
For standard inequalities involving just the variable without any additional functions, the usage would typically be without brackets, e.g., x < 3. It's possible instead the intent was to express a comparison involving x², where completing the square might simplify a quadratic inequality, such as 2 (x² - ¹)² ≤ 4. Once simplified, we can solve for x to find the range of solution.
For instance, if we have an inequality like 1.5≤ x ≤ 4.5, it means that the value of x is likely to be any number within that range inclusive of 1.5 and 4.5. In such cases, these boundaries represent the smallest and largest values that x can be, denoting that x is bounded between these values.