This discussion addresses the discrepancies in solving equations using different methods, specifically focusing on the equations 4 = 2(x + 2) + 2 and x - 3 = (x - 3)^2. The correct approach to the first equation involves subtracting 2 before dividing, while the second equation illustrates the importance of avoiding division by zero, which leads to the loss of a solution. The correct solutions for the second equation are x = 3 and x = 4, obtained by factoring after setting the equation to zero.
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If you divide both sides by 2, you get 2 = (x + 2) + 1, so that's a valid step, but a little longer than if you had subtracted 2 from each side as the first step.Scheuerf said:when solving 4 = 2(x + 2) + 2, I noticed that only get a correct answer when subtracting the two before dividing the other two.why is this?
If you bring all terms to one side, you get (x - 3)2 - (x - 3) = 0, which I suppose is what you mean by "setting it equal to 0." One way to continue is to factor the left side, which results in (x - 3)[x - 3 - 1] = 0, or (x - 3)(x - 4) = 0. The solutions are x = 3 or x = 4.Scheuerf said:I'm also confused about solving x - 3 = (x - 3)^2. You can get the right answer by setting it equal to 0. You then get two answers. If you just divide both sides by x - 3 and continue solving, you only get one answer. Why?