Answer:
a = -4
Step-by-step explanation:
To solve an equation like this, it works well to put all the variable terms on one side of the equal sign and all the constant terms on the other side.
To that end, it usually works well to locate the variable term with the smallest (most negative) coefficient, then subtract that quantity from the equation. Here, that term is "a" on the left side of the equal sign. When we subtract "a" from the equation, we get ...
... -15 = 3a - 3
Now, we have an unwanted constant on the right side of the equal sign. We want to add the opposite of that value to the equation. When we add +3 to the equation, we get ...
... -12 = 3a
Here, the variable and constant terms are separated the way we want, but the variable term has an unwanted coefficient. We can divide the equation by that value:
... -12/3 = (3a)/3
... -4 = a
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<em>Alternate method</em>
The method described above requires you exercise some judgment and identify the various kinds of terms in the equation. A more "mechanical" method can be the following:
1. Subtract one side of the equation from both sides.
... (a -15) -(4a -3) = 0
... -3a -12 = 0
2. Divide the equation by the coefficient of the variable.
... (-3a -12)/-3 = 0
... a + 4 = 0
3. Add the opposite of the constant to both sides of the equation.
... a = -4
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<em>Comment on this method</em>
This always works, though it may be a bit different than what your teacher or friends may show you.
Sometimes, as here, the variable coefficient can end up negative, so if you're confused by negative numbers, you may have to be careful to choose which side of the equation is subtracted. As above, choosing to subtract the side with the smallest variable coefficient ensures the result will have a positive variable coefficient.
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In general, to get rid of an added term you don't want, add its opposite to the equation. To get rid of a multiplier you don't want, divide the equation by that value. Remember: <em>whatever you do to one side of the equation, you must also do to the other side. This is what keeps the equal sign valid.</em>
