One solution means that x will only equal one number.
Many solutions means that no matter what number you replace x with, the equation will still be true.
No solution means that no matter what number you replace x with, the equation will be false, as both sides will not match.
One solution: x - 2 = 12
Check: Isolate the variable, x. Add 2 to both sides. Note the equal sign, what you do to one side, you do to the other:
x - 2 (+2) = 12 (+2)
x = 12 + 2
x = 14
Many solution: x + 3 = 3 + x
Check: Plug in numbers for x. If no matter what number you plug in, the equation is true, there is infinite amount of solutions:
If x = 1:
1 + 3 = 3 + 1
4 = 4
If x = 2:
2 + 3 = 3 + 2
5 = 5
etc.
No solution: x - 1 = x + 5
Check: No matter what number you plug in for x, both sides of the equation will not match. Check:
If x = 1:
1 - 1 = 1 + 5
0 ≠ 6
If x = 2:
1 - 2 = 2 + 5
-1 ≠ 7
etc.
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