Question

When you solve the equation x+9=15, how do you know what number to subtract from both sides? Why is it important to subtract the same number from both sides of the equation?

Answer 1

to solve equation with 1 variable, you need to separate variable on one side and the number to the other side so you can get the answer, that's the reason you nick to pick which number to subtract...ex
for your equation...x+9 on the left side, so to separate x, you need to subtract 9 ...to get x alone

and the second part is each equation have equal sign, so in order to balance to keep both side equal, if you do something to one side, you have to do exactly the same thing to the other side.