Compare and contrast simplifying the numeric expression 3 – (2 + 5) to the algebraic expression 3x – (2x + 5).
The numeric expression 3-(2+5) can be simplified by using the Order of Operations rules (Please Excuse My Dear Aunt Sally).
First you must simplify inside the parentheses --> (2+5)=7
We are left with the single operation 3-7--> 3-7 = -4
This simplified expression is -4.
The Algebraic Expression 3x-(2x+5) must be simplified differently. You can't simplify inside the parentheses because 2x and the constant 5 are not like terms.
Using the Distributive Property we can simplify this expression to 3x-2x-5.
We can now combine the like terms to get x-5
This simplified expression is x-5
When you simplify 3-(2+5) all the terms are constants so the result is a constant.
Thus the result is -4.
When you simplify 3x-(2x+5), you need to group the x terms or variable terms and the constants separately.
Thus the simplest form of this expression is x-5.