Simplify the following algebraic expression: 3X - (2 - X).
Could you please explain the steps that I take when simplifying algebraic expressions such as this one? Thanks.© BrainMass Inc. brainmass.com December 24, 2021, 4:52 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
By "simplifying" an algebraic expression, we mean writing it in the most compact or efficient manner, without changing the value of the expression. This mainly involves collecting like terms, which means that we add together anything that can be added together. The rule here is that only like terms can be added together.
Negative signs in front of parentheses:
3X - (2 - X)
In this problem, notice that the minus sign appears in front of the parenthesis. This is considered a special case, when a minus sign appears in front of parentheses. At first glance, it looks as though there is no factor multiplying the parentheses, and you may be tempted to just remove the parentheses. What you need to remember is that the minus sign indicating subtraction should always be thought of as adding the opposite. This means that you want to add the opposite of the entire thing inside the parentheses, and so you have to change the sign of each term in the parentheses.
Another way of looking at it is to imagine an implied factor of one in front of the parentheses. Then the minus sign makes that factor into a negative one, which can be multiplied by the distributive law:
3x - (2 - x)
= 3x + (-1)[2 + (-x)]
= 3x + (-1)(2) + (-1)(-x)
= 3x - 2 + x
= 4x - 2
Note, if there is only a plus sign in front of the parentheses, then you can simply erase the parentheses:
3x + (2 - x)
= 3x + 2 - x
Final comment about subtraction and minus signs: Although you can always explicitly replace subtraction with adding the opposite, as in this previous example, it is often tedious and inconvenient to do so. Once you get used to thinking that way, it is no longer necessary to actually write it that way. It is helpful to always think of minus signs as being "stuck" to the term directly to their right. That way, as you rearrange terms, collect like terms, and clear parentheses, the "adding the opposite" business will be taken care of because the minus signs will go with whatever was to their right. If what is immediately to the right of a minus sign happens to be a parenthesis, and then the minus sign attacks every term inside the parentheses.
I hope this helps.© BrainMass Inc. brainmass.com December 24, 2021, 4:52 pm ad1c9bdddf>