Question

(07.05 LC)

Which statement is true for the equation 4n − 3 = 4n − 2?

It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.

Answer 1

It has no solution.

Explanation:

If we try and solve it we end up with nonsense, so it has no solutions:

4n - 3 = 4n - 2

4n - 4n = - 2 + 3

0 = 1

- which is, of course, absurd.

Also, just by looking at the equation we can see that the term 4n -3 cannot in any way be equal to 4n - 2.

Answer 2

The answer is (A); there is no solution.

Explanation:

It doesn't require any calculations, really, just logic. Look, 4n = 4n wil be equal because they are the same numbers multiplied by the same variable - no matter the variable's value. However, if you subtract both values by different numbers, you won't get the same number:

Let's say n = 5

4n = 4n

= 4(5) = 4(5)

= 20 = 20

Now,

4n - 3 = 4n - 2

= 4(5) - 3 = 4(5) - 2

= 20 - 3 = 20 -2

= 17 ≠ 18

Hope this helps! Tell me if I was wrong!