Evaluating Algebraic Expressions

Learning Outcomes

  • Evaluate an expression for a given value


 Evaluate Algebraic Expressions

In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations.

To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

example

Evaluate
x+7x+7
when

  1. x=3x=3
  2. x=12x=12


Solution:

1. To evaluate, substitute
33
for
xx
in the expression, and then simplify.

x+7x+7
Substitute.
3+7\color{red}{3}+7
Add.
1010
When
x=3x=3
, the expression
x+7x+7
has a value of
1010
.

2. To evaluate, substitute
1212
for
xx
in the expression, and then simplify.

x+7x+7
Substitute.
12+7\color{red}{12}+7
Add.
1919
When
x=12x=12
, the expression
x+7x+7
has a value of
1919
.

Notice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for
xx
were different. When we evaluate an expression, the value varies depending on the value used for the variable.

 

try it



 

example

Evaluate
9x2,9x - 2,
when

  1. x=5x=5
  2. x=1x=1






 

try it



 

example

Evaluate
x2{x}^{2}
when
x=10x=10
.





 

try it



 

example

Evaluate 2x when x=5\text{Evaluate }{2}^{x}\text{ when }x=5
.





 

try it



 

example

Evaluate 3x+4y6 when x=10 and y=2\text{Evaluate }3x+4y - 6\text{ when }x=10\text{ and }y=2
.





 

TRY IT



 

example

Evaluate 2x2+3x+8 when x=4\text{Evaluate }2{x}^{2}+3x+8\text{ when }x=4
.





 

try it



In the video below we show more examples of how to substitute a value for variable in an expression, then evaluate the expression.



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