Question

Which of the following is an equation?
A. f(x) = 2x + 3
B. 2x + 3 = 4y + 5
C. x = y
D. Both B and C

Answer 1

Hint: An equation is an expression which expresses the relationship between two quantities which are equal to each other. The two quantities can be a constant or a variable. We will check all the options given in the question, to see if they are equations or not. An example of an equation is- x = 7y + 3

Complete step-by-step answer:
We have been given four options, and we need to determine which of them are equations. So we will proceed taking each option at a time successively.
In option A, we have been given that f(x) = 2x + 3. Although this may seem to be an equation due to the presence of the ‘equal to’ sign. But this expression does not compare the two comparable quantities. Rather, it is a ‘name’ for the function 2x + 3.
In option B, which is 2x + 3 = 4y + 5, two variable quantities are being compared with the presence of an ‘equal to’ sign, which means that this is an equation.
Just like in the previous option, in option C, which is x = y, two variable quantities are being compared so this is also an equation.
The option D states that both options B and C are equations, which is correct. Assuming that only one option among these can be correct, option D is the correct answer.
The correct option is D. Both B and C.

Note: We have a very minor distinction between what is an equation and what is not. Almost all the students may think that option A should also be correct. But we have to look closely here. The term on the LHS, f(x), is not a variable. Rather it is a name given to the quantity on the RHS, so this should not be considered as an equation.