When a question asks you to "evaluate" a situation, you are most likely being asked to find a numerical answer. The process is simple. Replace the variable in the expression or equation, with the numerical value you are given, and simplify the result.

hint gal
When evaluating an expression:
Remember to follow the proper order of operations and to watch out for those pesky negative signs.
smallstar Placing a set of parentheses around the value being substituted will help you avoid errors with signs.

Numeric Substitutions:
expin1
Evaluate 2x - 3, when x = 4.
   
Replace x with 4 and simplify.
   
2(4) - 3 = 8 - 3 = 5 Answer

expin2
Evaluate x2 - 1, when x = 5.
   
Replace x with 5 and simplify.
   
(5)2 - 1 = 25 - 1 = 24 Answer

expin3
Evaluate a2 + a, when a = 3.
 
   
Replace all values of a with 3 and simplify.
   
(3)2 + (3) = 9 + 3 = 12 Answer

expin4
Evaluate 6x + 3y, when x = 2 and y = 5.
   
Notice the use of two variables. Replace each and simplify.
    6(2) + 3(5) = 12 + 15 = 27 Answer

expin5
Evaluate x3 + 3x2 - 2x - 5, when x = -4.
   
Especially use parentheses when working with negative values.
   
(-4)3 + 3(-4)2 - 2(-4) - 5 = -64 + 48 + 8 - 5 = -13 Answer

expin6
Evaluate a2b + a, when a = -3 and b = 2.
bewareS
Do NOT write:
-32(2) + (-3) as this is
-9(2) + (-3) = -21
   
Parentheses are needed in this problem.
   
(-3)2(2) + (-3) = 18 + (-3) = 15 Answer


Algebraic Substitutions:

It may be the case that you will be asked to evaluate an expression using another expression.
Don't panic!!! Just follow the same process as you did when evaluating for a number.


expin7
Evaluate x2 + 2x - 4, when x = 2a.
   
Remember to use parentheses!
   
(2a)2 + 2(2a) - 4 = 4a2 + 4a - 4 Answer

expin8
Evaluate 3x + 10 when x = 3m + 15
   
Remember to use parentheses!
   
3(3m + 15) + 10 = 9m + 45 + 10 = 9m + 55 Answer



dash

The graphing calculator can also be used to evaluate expressions.
Click on the link at the right to see the possibilities.
ti84c
For calculator help with Evaluating Expressions
click here.

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