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Given, that
4x + 6 = 6x - 12; then,
(6x - 12) - (4x + 6) = 0,
2x - 18 = 0, and
2x = 18.
Thus, x = 9.
Checking, we substitute 9 for x in the equation:
4(9) + 6= 6(9) - 12; whence,
36 + 6 = 54 - 12, and
42 = 42, which is patently true.
What this means is that the original equation is true exactly when x = 9; otherwise, it is false. We call 'x = 9' the solution to the given equation.
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