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5x+9=-4x-45
We move all terms to the left:
5x+9-(-4x-45)=0
We get rid of parentheses
5x+4x+45+9=0
We add all the numbers together, and all the variables
9x+54=0
We move all terms containing x to the left, all other terms to the right
9x=-54
x=-54/9
x=-6
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