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You want to put the variable on one side of the equation and put the constant on the other side. To do that, you subtract the value you don't want where it is.
-15v - 40 = 23 - 8v
-40 = 23 - 8v - (-15v) (subtract -15v from both sides)
-40 - 23 = 7v (subtract 23 from both sides)
-9 = v (divide both sides by the coefficient of v)
-15v - 40 = 23 - 8v
-40 = 23 - 8v - (-15v) (subtract -15v from both sides)
-40 - 23 = 7v (subtract 23 from both sides)
-9 = v (divide both sides by the coefficient of v)
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