Not a solution I believe.
7(x-2) + 3(x + 2) = 5(x-6)...distribute thru the parenthesis
7x - 14 + 3x + 6 = 5x - 30...combine like terms
10x - 8 = 5x - 30...subtract 5x from both sides
10x - 5x - 8 = -30....add 8 to both sides
10x - 5x = -30 + 8...combine like terms
5x = - 22
x = -22/5 = - 4 2/5 <==
For any equation with more than one variable, there is either no solution or infinitely many solutions.
If we can find just <em>one</em> solution that works, that would eliminate the possibility of there being no solution, and so we could prove it to have infinitely many solutions.
Can we come up with at least one solution to these equations? Of course!
For x=y
Thinking of two equal numbers is extremely easy. For instance, if we chose x to be 2 and y to be 2, that's a solution right there! Thus x=y has infinitely many solutions.
It's just as easy picking two numbers that are equal when you multiply them by 1.25. Think back to the multiplication property of equality. If two things are equal, and you multiply them by a number, they will still be equal. So all we need is, once again, two equal numbers. 2 and 2, boom and boom. 1.25x=1.25y has infinitely many solutions as well.
