Compare and contrast simplifying the numeric expression 3 – (2 + 5) to the algebraic expression 3x – (2x + 5).

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flbyrne's profile pic

flbyrne | (Level 3) Assistant Educator

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When you simplify 3-(2+5) all the terms are constants so the result is a constant.

3-2-5=-4

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.

3x-2x-5=x-5

Thus the simplest form of this expression is x-5.

chadbutler's profile pic

chadbutler | High School Teacher | (Level 1) Adjunct Educator

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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

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