Which of these expressions represents a linear equation?

• A. x^2 + 3 = 0
• B. 2x + 1 = 0
• C. x + 1/x = 2
• D. √x + 5 = x

Answer: (B)

A linear equation is characterized by having variables raised only to the first power and no products of variables, such as (xy). In this case, the expression that meets these criteria is the one that can be rewritten in the standard form of a linear equation.

The expression that represents a linear equation is (2x + 1 = 0). This equation consists of the variable (x) raised to the first power, making it linear. The form shows a direct relationship between (x) and the constant term. Linear equations can be graphed as straight lines, which is a crucial property distinguishing them from nonlinear equations.

In contrast, the other expressions involve higher powers or the combination of terms that make them nonlinear. For example, the first expression involves (x) raised to the second power ((x^2)), making it a quadratic equation. The third expression contains the variable in both a linear and a fractional form, which leads to a non-linear relationship. Lastly, the fourth expression has (x) under a square root, which also makes it non-linear. Only the second option, with its first-degree term in (x), qualifies as a linear equation.