Question

How many solutions does this equation have? a+3+2a=-1+3a+4

Answer 1

Let's start by cleaning up this equation to make it easier to read by putting all the variables on one side and everything else on the other side using subtraction and addition. Then simplify.
1) Original equation 
a + 3 + 2a = -1 + 3a + 4

2) Subtract 3 from both sides
a + 2a = -3 - 1 + 3a + 4

3) Subtract 3a from both sides
a + 2a - 3a = -3 - 1 + 4

4) Simplify
3a - 3a = -4 + 4
0 = 0

Since 0 = 0 is always true, this equation as an unlimited number of solutions. No matter what you put in for the variable a, it will all cancel out, and you'll get 0 = 0!

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Answer: Infinite number of solutions