Evaluating Variables and Expressions
To evaluate an expression with variables, substitute the given value for each variable and then follow the order of operations. Substituting first and simplifying second is what keeps the work reliable. The examples below show the method, with practice problems and answers.
Evaluating Variables and Expressions: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Name the variableChoose a letter for the unknown quantity.
- Translate in chunksTurn each phrase into an operation, keeping order words attached.
- Simplify or evaluateCombine like terms or substitute the given value.
Worked examples
Translate a phrase
- Let the number be x.
- Twice the number is 2x.
- Seven more than that adds 7.
Evaluate carefully
- Replace x with 5.
- Multiply before subtracting.
- Compute 15 – 4.
Try one before moving on
Evaluating Variables and Expressions: pop-up practice
With the expression (x+3), then (3) is known as a constant since it doesn’t vary, and the (x) is known as a variable since it can change. (When giving a name to the variable, disregard any exponents or radicals, including the variable.)
Algebraic expressions are a group of constants and variables joined together via algebraic operations of subtraction, addition, division, and multiplication.
Variables are letters, for instance, (x, y) or (z), which signify an undetermined number.
Any variable within an algebraic expression can take on or be designated various values. Whenever that occurs, the value of that algebraic expression will change.
When evaluating an algebraic expression, it means you have to figure out the expression’s value for a given value of each of the variables within the expression.
If you are aware of the variables’ values, it’s possible to replace the variables with their values, then evaluate your expression.
Related Topics
How do you evaluate variables?
STEP one: Switch each variable in your expression with its given value
STEP two: Simplify the resultant expression utilizing the order of operations.
STEP three: If this algebraic expression comprises over one variable, substitute each variable with the assigned value, then simplify the expression like before.
Evaluating Variables – Example 1:
Simplify. (a-1, a=4)
Solution:
We place the value of the variable in the expression: (a-1=4-1=3)
Evaluating Variables – Example 2:
Simplify. (2x+y, x=2, y=3)
Solution:
Substitute (2) for (x), and (3) for (y), then:
(2x + y =2 (2) + 3 =4 + 3=7 )
Exercises for Evaluating Variables
Simplify each algebraic expression.
- (color{blue}{x + 3y – 1, \ x = 1, y = 3 } \)
- (color{blue}{3a – 4, \ a = 4} \ )
- (color{blue}{5 + 5x – y, \ x = 1, y = 3} \ )
- (color{blue}{x + 15, \ x = 10} \ )
- (color{blue}{2 – 2x +y, \ x = 7, y = 2} \ )
Answers
- (color{blue}{9})
- (color{blue}{8})
- (color{blue}{7})
- (color{blue}{25})
- (color{blue}{14})
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