Question

What is a two-step equation with no solution?

Answer 1

Okay forget that. Try to solve this:

x + 3 = x + 5

Answer 2

I'm sorry to hear that.

Answer 3

Don't you have to subtract from both sides?

Answer 4

Yes, you subtract something from both sides. Any clue what?

Answer 5

3?

Answer 6

Okay, so subtract 3 from both sides. What do you end up with afterwards?

Answer 7

x=x+2

Answer 8

Okay, so the next step is to attempt to put like terms on the same side. In other words, you have to attempt to place all the x's on one side and keep all the numerals on the other side. Any idea on how you might do that?

Answer 9

Add maybe?

Answer 10

You can't just add anything to both sides. The goal is to attempt to isolate x. You have x on one side, but there's an x on the other side. Both x's need to be on the same side. There's only one way to do that...or at least attempt to. Figuring out the right operation to use is key here.

Answer 11

So what would I do..?

Answer 12

Just think about it a little more.

Answer 13

I have been, this whole time. Could you help me maybe?

Answer 14

Well, there's really no other way to demonstrate it without revealing the answer, but I'll at least attempt to explain.

An equation will have no solution if there is no value of x that will satisfy both sides.
If you have an equation where the same term involving x is applied to both sides, then that increases the chances that there is no solution.


If you have 2x = 2x, the solution to that is any real number. However, if you intentionally add to different numbers to both sides, then that is a violation of algebra. Say for example, you add 3 to one side, and 5 to the other side:

2x + 3 = 2x + 5

Now you have created a situation that guarantees there won't be any solution.

If you tried to solve that, in the first step you would subtract 3 from both sides. The second step, you would subtract 2x from both sides.

You would end up with

0 = 5

Which is not true. In other words, there is no solution since it is not possible to isolate or solve for x.

Answer 15

@chloenicole

Answer 16

That helped me so much. Thank you!

Answer 17

Glad you understood.