What is the answer to the inequality 4x plus 2y equals 40?

Answer 1

First of all, the word "equals" doesn't belong in an "inequality".

Let's assume you actually meant to call it an "equation".

Now, we have the nagging felling that you're not exactly sure what you mean by "answer",

so we'll tell you: It means a pair of numbers that you can put in the places of 'x' and 'y'

that make the whole equation a true statement.

For example:

Can 'x' be 1 and 'y' be zero ?

If they are, you'd have 4(1) + 2(0) = 40. Is that a true statement ?

Well, it says that 4 = 40, which is a big fat lie, so 'x' can't be 1 when 'y' is zero.

Can 'x' be zero and 'y' be 20 ?

If they are, then you have 4(0) + 2(20) = 40. Is that a true statement?

Well, it says that 40 = 40, which is true, so 'x' can be zero when 'y' is 20,

and that's a good 'answer'..

But wait. You're not done. We want you to try another one:

Can 'x' be 5 and 'y' be 10 ?

If they are, then you have 4(5) + 2(10) = 40. Is that a true statement ?

Well, it says that 20 + 20 = 40, and that's true, so 'x' can be 5 when 'y' is 10.

That's another good answer.

How many answers can this thing have ? We're sure that if you're still reading,

you're about to be surprised.

Your equation ... [ 4x + 2y = 40 ] ... is the equation of a straight line.

Every point on the line is an 'answer' to the equation.

How many points are there on a line ? An infinite number of them.

Your equation has an infinite number of correct 'answers'.

And also an infinite number of wrong answers ... all of the points that aren't on the line.