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# 3(x+1)+1+2x+2x=2(2x+2)+x

3(x+1)+1+2x+2x=2(2x+2)+x

1st distribute the 3 into the paraentheses 3(x) and 3(1) and
at the same time distribute the 2 into the (2x+2) to get 2(2x) and 2(2) rewrite the equation

3x +3 +1 +2x +2x = 4x +4 +x, the bold lettering is the "new" stuff

2nd: combine like terms on each side but not together(remember like terms have the same variable so x terms with x terms and no x numbers with no x numbers)

3x +3 +1 +2x +2x = 4x +4 +1x  ----> 7x +4 = 5x +4  The underline terms were combined, the italics  terms were combined and the bold terms combined.

Now let's take a look at this equation.    7x +4 = 5x +4.  Is there any number that you can multiply by 5 or 7 and add 4 and get the same number? yes and let's find it.

since there is a 4 on each side of the equals sign we will subtract 4 from each side.

7x +4 - 4 = 5x +4 - 4  -----> 7x +0 = 5x + 0 ----> 7x = 5x

now think about this again. Is there a number that we can multiply by 7 and by 5 and get the same results?

Let's keep going.

7x = 5x, subtract 5x from both sides.        7x - 5x = 5x - 5x     ------>      2x = 0

2 times what number is 0?   or algebraically:    2x = 0, divide each side by 2.    2x /2 = 0/2 ---> x = 0

Please notice how whenever I reduced the equation I performed an operation(plus, minus, mult., divide) to BOTH sides identically.

recheck:
3(0+1) +1 +2(0) +2(0) = 2(2(0) +2) + 0 ----> 3(1) +1 +0 = 2(0+2) + 0 ---> 3 + 1 = 2(2)--->4=4, true!