Evaluating Algebraic Expressions
Hi everyone. This math educational post is on evaluating algebraic expressions. This particular topic may not be fun and does not have real world applications. The thing is though is that this is an important algebra topic for early high school math students.
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Topics
- Algebra Expressions
- Substitution of Values
- Following Order of Operations
- Harder Cases
Algebra Expressions
An algebra expression is a quantity which contains a combination of numbers and unknown quantities. Examples include 2x, x + 7, 10x - 4, and x + pi. Note that an algebra expression does not contain an equal sign. There is no need to isolate for a variable.
Substitution Of Values
When it comes to evaluating algebraic expressions, the concept of substituting unknown quantities (variables) with known values comes into play.
In the algebraic expression x + 5, substituting x = 5 into x gives 5 +5 which is equal to 10. Substituting a different value such as 2 gives 2 + 5 = 7 which is a different value.
When it comes to with more than one variable, you would need to be given values for those unknown variables. For example, substituting x = 2 and y = 1 in the algebraic expression of xy - 2y + 3x gives the following:
Following Order Of Operations
With evaluating algebraic expressions, do remember that the algebra steps follows the order of operations. BEDMAS is for Brackets, Exponents followed by Division, Multiplication, Addition and Subtraction. Whenever there is a tie in multiplication and division, perform the operation that is first from left to right. Do the same with ties between addition and subtraction.
Example One
Substituiting x = 2 in the algebraic expression 5x - 1 gives:
Example Two
Given the algebraic expression of 2(3x - 1) - 4, what would the expression be if x = -1?
Example Three
Substitute x = 0.5 in the expression 
.
Harder Cases
Evaluating algebraic expressions can get really difficult and messy. Here are some harder examples.
Example One
Substitute x = 1, y = 10 in the following expression.
Solution
Example Two
Substitute x = 1, y = -1, z = 2 in the following expression.
Solution
This solution involves a lot of negative numbers so be careful.
Practice Problems With Solutions
Find the value of 3x - 1 when x = 3.
Find the value of y^2 + 2y - 1 when y = -1.
Given the expression of xyz - 2y where x = 0.5, y = -0.5 and z = 8.
Find the value of the expression
where x = 10 and y = 2.Determine the value of the expression below when x = -1, y = 2, z = 3.
Solutions
Here are the solutions to the above practice problems.
8
-2
With x = 0.5, y = -0.5 and z = 8, xyz - 2y becomes -2 - 2 (-0.5) = -2 + 1 = -1
10
Determine the value of the expression below when x = -1, y = 2, z = 3.
Solution
