3×x

3×x denotes the product of the constant 3 and a variable x. In algebra, x stands for a real (or complex) number, and the expression 3×x represents three times that number. The same expression is commonly written as 3x, and is equivalent to x×3, illustrating the commutativity of multiplication.

As a monomial of degree 1 with coefficient 3, 3x is a linear term. If x is treated as a function argument, the corresponding linear function is f(x) = 3x. In polynomials, the expression 3x is the simplest non-constant term; its degree is 1 and its leading coefficient is 3.

Algebraic rules: 3×(a+b) = 3a + 3b (the distributive property). (3)(ab) = (3a)b, and more generally scalar multiplication by 3 is compatible with standard multiplication. It also satisfies 3×0 = 0 and 3×1 = 3. Multiplying by 3 is a scalar operation and acts as a linear transformation on real numbers, mapping x to 3x.

Graphically, if y = 3x, the graph is a straight line through the origin with slope 3. The y-intercept is zero, and the slope indicates the factor by which the input x is scaled.

In other contexts, 3×x appears in solving linear equations, modeling proportional relationships, and in modular arithmetic where the product 3x is taken modulo n. The notation 3×x emphasizes the product form, while 3x is the more common handwritten or typeset variant.