Question

consider the equation -5x=10x+3=5x+6 would it have one solution, no solutions, or infinitely many solutions

Answer 1

Alright, let's start by simplifying.


`-5x+10x+3=5x+6`

Let's get all of the variables on one side.
Subtract 5x from each side to clear the right.


`-5x-5x+10x+3=6`

We could also subtract out that 3...


`-5x-5x+10x=3`

Combining like terms!
If we have 10x, and then subtract 5x and 5x...we're left with zero!


`0=3`

However, this equation can't be true!
Since this always boils down to 0=3 (the variables don't even matter)...
There are no solutions for x that could even make the equation true!