We can describe $15x - 10$ as an expression. Would we describe $6x - 2 < 35$ as an expression or an inequality?
Answer (2)
The problem requires classifying the statement 6 x − 2 < 35 . Since it contains a 'less than' sign, it is classified as an inequality. Therefore, the answer is inequality. $\boxed{inequality}
Explanation
Understanding the Problem The problem states that 15 x − 10 is an expression and asks us to classify 6 x − 2 < 35 . We need to determine whether 6 x − 2 < 35 is an expression, an equation, or an inequality.
Definitions An expression is a combination of variables, numbers, and operations without an equality or inequality sign. An equation is a statement that two expressions are equal, indicated by an equals sign (=). An inequality is a statement that compares two expressions using inequality signs such as <, >, ≤, or ≥.
Classification The statement 6 x − 2 < 35 contains the 'less than' sign (<), which indicates that it is an inequality.
Examples
In real life, inequalities are used to describe constraints or limitations. For example, if you have a budget of $50 for groceries, you can represent the total cost of your items as an inequality: total cost < $50. This helps you ensure that you don't exceed your budget while shopping. Inequalities are also used in various fields like engineering, economics, and computer science to model and solve problems involving constraints and optimization.
The statement 6 x − 2 < 35 is classified as an inequality because it uses a less-than sign for comparison. In contrast, 15 x − 10 is simply an expression. Hence, the answer is inequality.
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