Question 168843
you want to get all the x variables on one side of the equation and you want to get all the constants on the other side of the equation.
you do this by adding or subtracting from both sides of the equation.
here's how it works:
your equation is:
5x - 3 = 13 - 3x 
you want to get the 3x from the right side of the equation to the left side of the equation.
you do it by adding 3x to both sides of the equation.
equation becomes:
5x - 3 + 3x = 13 - 3x + 3x
you can see that the - 3x and + 3x on the right side of the equation cancel out so the equation becomes:
5x - 3 + 3x = 13
when you combine like terms, the equation becomes:
8x - 3 = 13
now you want to move the -3 over to the right side of the equation.
you do it by adding 3 to both sides of the equation.
8x - 3 + 3 = 13 + 3
when you combine like terms, the -3 and + 3 on the left side of the equation cancel out and you get:
8x = 13 + 3
which becomes:
8x = 16
you divide both sides of the equation by 8 to get
x = 16/8 = 2
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you substitute 2 for x in your original equation:
5x - 3 = 13 - 3x
becomes:
5*2 - 3 = 13 - 3*2
which becomes:
10 - 3 = 13 - 6
which becomes:
7 = 7
since this is true, the value of x = 2 is good.
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when you combine like terms, you are adding together all the terms that have the same variable.
5x + 6x + 3x = 14x
they are like terms because they are all multiples of x.
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similarly, if you have:
5x^2 - 3x + 2x^3 + 15x - 20x^2
you would combine like terms as follows:
5x^2 - 20x^2 = -15x^2
-3x + 15x = 12x
2x^3 doesn't have anything to combine with.
your final combined terms are:
2x^3 - 15x^2 + 12x