Quandaries and Queries


i need help with solving equations and formulas such as
-3x+b=6x, for x. I do not understand how you find x.




Hi Lonnie,

I find that it helps to think of an equation as a scale. One that you might find in the physics lab, with a pan on each sides. In your case you have -3x+b on one side and 6x on the other. The equal sign means that they balance. The object is to perform "legitimate" operations and end with just x on one side and something not involving x on the other side.

What are "legitimate" operations? I can add of or subtract weights from either side as long as I maintain the balance. That means I can add the same amount to both sides or subtract the same amount from both sides. I can also multiply both sides by the same amount or divide both sides by the same amount since this will also maintain the balance.

Your equation is

-3x + b = 6x.

I want to arrive with an equation that has only x on the right side so I need to eliminate the -3x from the left side. I do this by adding 3x to both sides. This maintains the balance and gives me

-3x + b + 3x = 6x + 3x

Simplifying I get

b = 9x

I am almost there. I want x on the right side and I have 9x, hence I am going to divide both sides by 9. This gives


Which is

 b/9 = x

Thus I know that x is b/9.



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