Break Down the Algebraic Expression: Understanding 6x

To solve this problem, we'll clearly delineate the expression $6x$ as follows:

• The number 6 is the coefficient.
• The letter $x$ is the variable.
• These two components are connected by multiplication, represented as $6 \cdot x$.

Thus, the expression $6x$ is equivalent to $6 \cdot x$, where 6 is multiplied by $x$.

Examining the choice options:

• Choice 1: $6\cdot x$ is correct because it represents the expression as a product of the coefficient and the variable.
• Choice 2: $x \cdot x \cdot x \cdot x \cdot x \cdot x$ represents a repeated multiplication of $x$, not applicable here.
• Choice 3: $\frac{6}{x}$ represents division, not the required approach.
• Choice 4: Incorrect, as $6x$ can indeed be expressed as $6 \cdot x$.

Therefore, the best breakdown of the expression is $6 \cdot x$, matching choice 1.