These "3-step" equations can be solved a variety of ways. One that always works is the following:
- Locate the variable term with the smallest coefficient. (3x, on the left)
- Subtract everything on that side of the equation from both sides of the equation. Simplify. (0 = 2x +42)
- Divide by the coefficient of the variable. (0 = x + 21)
- Add the opposite of the constant. (-21 = x)
The solution is x=-21.
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Check
3(-21)-10 = 5(-21)+32 . . . . . . substitute -21 for x in the given equation
-63 -10 = -105 +32
-73 = -73 . . . . . . the solution works in the original equation
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* Note that the reason for the "step 1" listed here is to make sure the resulting coefficient of the variable is positive. You could arbitrarily always subtract the right side, for example, but then in step 3 you would be dividing by a negative number sometimes. That works just fine and will give you the correct answer, but some folks get confused doing arithmetic with negative numbers. The steps listed help avoid that confusion.
