Final answer:
The linear equations from the options given are a) 3x + 5 = 0 and c) 2(4x + 1) = 3 - (2x + 4), because they can be simplified to the form y = mx + b, where x and y are raised only to the first power.
Step-by-step explanation:
To determine which equations are linear equations, it is imperative to recognize that a linear equation can be represented in the standard form y = mx + b, where m and b are constants, and x and y are variables. The crucial property is that x and y must appear to the first power only and not be multiplied together or by any other variable.
- a) 3x + 5 = 0 is a linear equation because it can be rearranged to fit the form y = mx + b, with y being 0 in this case.
- b) (x - 2)(2x + 3) = 0 is not a linear equation because when expanded it would yield a quadratic term (x^2).
- c) 2(4x + 1) = 3 - (2x + 4) is a linear equation. If you distribute and simplify it, you get a form of y = mx + b.
- d) 3√x - 1 = 6 is not a linear equation because the variable x is under a square root, changing the degree of the equation.
The linear equations from the options given are a) 3x + 5 = 0 and c) 2(4x + 1) = 3 - (2x + 4).