Question

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$3 x+2 \leq 8$$

Short answer

The given mathematical statement '3x + 2 ≤ 8' is an inequality.

Step-by-step solution

Identify Mathematical Characteristics

In mathematical terms, an expression is a group of symbols representing a value or relationship. It does not involve equal or inequality signs, but may include numbers, operations, and variables. An equation, on the other hand, is a statement that establishes the equality of two expressions. It contains an equals sign (=). An inequality is a relation that holds between two values when they are different. Inequalities use symbolic notation (>, <, ≥, ≤) to compare two quantities or expressions. The given mathematical statement uses the less than or equal to symbol, so it is not an expression or an equation.

Confirm Inequality

Because the given mathematical statement '3x + 2 ≤ 8' uses a less than or equal to symbol (≤), it is an inequality. It is making a comparison between '3x + 2' and '8' and stating that '3x + 2' is less than or equal to '8'.