3x

In mathematics, the expression 3x denotes the product of the constant 3 and the variable x. It is a linear monomial in x, having degree 1 with respect to x.

The term appears in polynomials and equations such as 3x + 2, ax + b, or 3x = 9. Here x represents a variable that can take real or complex values; when x is a number, 3x is three times that number. In vector contexts, 3x can also denote scalar multiplication of a vector x by 3.

Evaluating 3x is straightforward: if x = 4, then 3x = 12. If x = 0, then 3x = 0. In general, solving an equation with 3x involves dividing by 3, provided the equation is consistent with real or complex numbers. For example, 3x = 9 gives x = 3.

Properties and operations: Distributive property yields a(3x) = (3a)x and 3(x + y) = 3x + 3y. Factoring allows 3x + 9 to be written as 3(x + 3). When solving linear equations, the coefficient of x can be manipulated to isolate x, such as in 3x = 9 leading to x = 3.

Graphical interpretation: In a relation y = 3x + b, the slope is 3, meaning the line rises three units for every one unit increase in x. If b = 0, the graph passes through the origin, corresponding to the expression 3x alone.

Summary: 3x is a fundamental linear term representing three times a variable or vector, used across algebra, calculus, and geometry to express scaled quantities and linear relationships.