You can simplify 3x - 1 - 1 as 3x - 2.
In an algebraic expression as this one, one can combine (add or subtract) only the terms that are called "like terms".
For example, 2x and -4x are like terms because they both contain variable x with the same power 1. However, 2x and x^2 are not like terms because they contain x with different exponents, so they cannot be combined. Also, 2x and y, or x and 2 are not like terms.
In expression 3x -1 - 1, 3x and 1 are not like terms, but -1 and -1 are, because all numbers are like terms. To combine -1-1, recall that when subtracting a positive number (second 1) from the negative one (-1), the result will be negative and absolute values of the numbers add up: -1 - 1 = -2.
So, 3x -1 - 1 =3x - 2.
3x-1-1 simplifies down to 3x - 2
this is because 3x and -1 are not like terms therefore they can't' be added together. Yet -1 and -1 can be added together because they are common terms.
This is as much as you can do, once you get to 3x - 2 you can no longer add or subtract because the terms are not the same, neither can you factor out.
3x-1-1 would simplify to 3x-2 because in such expressions we are supposed to combine like terms. The numbers don't have any variables with them so they are considered like and get added together but the 3x remains as it is because there are nothing that is like in the expression.
All numbers without a variable are like terms. for example: 3, -5, 7, 2 etc
All numbers with a similar variable are like terms. for example: 3x and 4x but 5a and 6g are not like because its not the same letter.
Hope that helps. :)
3x-1-1 would simplify down to 3x-2.
My algebra teacher told us to assign a fruit to each variable (apples for an x^2, oranges for just an x, and peaches for numbers without a variable). In this case, the 3x would be an orange and the -1's would be peaches. She told us that we could not combine apples and oranges (or oranges and peaches in this case), but like fruits can be combined. After combining the like terms, you find that -1+-1=-2. After that process is complete, you reach the final answer of 3x-2.