> Give me "x + (x + 1) + (x + 2) = 69" and I wouldn't know where to start.
You memorize a few rules about what things you're allowed to do, then you apply the rules to simplify the problem in front of you. Sometimes, the hard part is that you don't know one of the rules you need to know. Other times, it's figuring out which of the rules you need to know that you should use. By practicing lots of problems, you get a good intuition for which direction to go, but it's not uncommon with more difficult problems to take the wrong way and end up confused.
First, we're allowed to drop the parentheses with addition (the "associative" rule for addition), so
x + x + 1 + x + 2 = 69
Now we put the similar terms together:
x + x + x + 1 + 2 = 69
How many Xs do we have? Three. Another way of writing that is 3x. So replace that part. Also, 1+2=3, so we'll replace that as well. "Apply rule and replace" is pretty much the most fundamental mathematical operation.
3x + 3 = 69
Let's get rid of the 3 by subtracting it from both sides to keep the equation balanced. On the left side the 3 cancels out (that's why we did this). On the right, we get 69-3, which is 66.
3x = 66
At this point, we just divide by 3 and simplify.
x = 66/3
x = 22
Our numbers are x (22), x+1 (23) and x+2 (24) according to how we listed them in the original problem.
You memorize a few rules about what things you're allowed to do, then you apply the rules to simplify the problem in front of you. Sometimes, the hard part is that you don't know one of the rules you need to know. Other times, it's figuring out which of the rules you need to know that you should use. By practicing lots of problems, you get a good intuition for which direction to go, but it's not uncommon with more difficult problems to take the wrong way and end up confused.
First, we're allowed to drop the parentheses with addition (the "associative" rule for addition), so
x + x + 1 + x + 2 = 69
Now we put the similar terms together:
x + x + x + 1 + 2 = 69
How many Xs do we have? Three. Another way of writing that is 3x. So replace that part. Also, 1+2=3, so we'll replace that as well. "Apply rule and replace" is pretty much the most fundamental mathematical operation.
3x + 3 = 69
Let's get rid of the 3 by subtracting it from both sides to keep the equation balanced. On the left side the 3 cancels out (that's why we did this). On the right, we get 69-3, which is 66.
3x = 66
At this point, we just divide by 3 and simplify.
x = 66/3 x = 22
Our numbers are x (22), x+1 (23) and x+2 (24) according to how we listed them in the original problem.