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

1 Answer

2 votes
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!

User QurakNerd
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