Question

Write one equation that has one solution, one equation that has no solution, and one solution that has infinitely many solutions

(hopefully a actual person answers this time and not a bot trying to grab my ip)

Answer 1

Explanation:

one solution

2(x+3)-3x=-2x+10

infinite solution

2(x+5)+6x=8x+10

no solution

3(x+2)=3x+7

Answer 2

One Solution:

You can do something simple like:

x = 4

Or you can take that x=4 and add 7 to both sides:

x + 7 = 11

Or you can take that and multiply by 3 on both sides:

3x + 21 = 33

They all have one solution, 4.

No Solution

Take a false statement like, which has no solution:

3 = 6

Add the same thing, say 3x, to both sides and it still has no solution:

3x + 3 = 3x + 6

You could factor the left side to make it look fancier:

3 ( x + 1 ) = 3x + 6

All of those have no solution.

Infinitely Many Solutions

Just like the "no solution, but start with a statement that is alwasy true:

3 = 3

Add the same thing, say 3x, to both sides and it still has no solution:

3x + 3 = 3x + 3

You could factor the left side to make it look fancier:

3 ( x + 1 ) = 3x + 3

All of those have an infinite number of solutions.