SOLUTION: how do you find "x" in a equation like 2x-3=5x+12 ???

Question 167310: how do you find "x" in a equation like
2x-3=5x+12
???
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
you want to get all your x's on the same side of the equation.
you do this by any of the following:
1. add or subtract the same value to both sides of the equation.
2. multiply or divide each side of the equation by the same value.
3. raise both sides of the equation by the same power.
all of these operations, if done properly, do not change the value of the equation.
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in your problem, you start off with:
2x-3 = 5x + 12
you want to move all your x's to the left side of the equation or the right side of the equation.
let's try the right.
you subtract 2x from both sides of the equation.
2x - 3 - 2x = 5x - 2x + 12.
when you combine like terms, the 2x on the left side of the equation cancels out.
combining like terms, you get:
-3 = 3x + 12.
now you want to move the 12 from the right side of the equation to the left side.
you do this by subtracting 12 from both sides of the equation.
-3 - 12 = 3x + 12 - 12.
when you combine like terms, the 12 on the right side of the equation cancels out.
combine like terms, you get:
-15 = 3x
now you need to divide both sides of the equation by 3.
-15 / 3 = 3x / 3
completing the operation, you get:
-5 = x
this is the same as:
x = -5
that should be your answer.
substituting -5 for x in your original equation gets:
2x-3=5x+12
(2*-5) - 3 = (5*-5) + 12
-10 - 3 = -25 + 12
-13 = -13
since the 2 sides of the equatin are equal, the value of x = -5 is true.
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