How to Evaluate an Algebraic Expression
Identify the parts of an algebraic expression., Understand what a variable is., Determine how to evaluate the expression., Identify the variable and its value., Substitute the given value for the variable., Complete the necessary calculations...
Step-by-Step Guide
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Step 1: Identify the parts of an algebraic expression.
An algebraic expression is a set of numbers and letters combined by mathematical operations, such as addition, subtraction, division, and multiplication.
The numbers in the expression are called constants or coefficients, depending on their function.
The letters are called variables.2x{\displaystyle 2x} is an expression.
In this expression, you are multiplying the coefficient 2{\displaystyle 2} by the variable x{\displaystyle x}. 2x+3y{\displaystyle 2x+3y} is an expression called a binomial.
In this expression, you add the product of 3y{\displaystyle 3y} to the product of 2x{\displaystyle 2x}.
In this expression, 2{\displaystyle 2} and 3{\displaystyle 3} are coefficients, and x{\displaystyle x} and y{\displaystyle y} are variables.
Once you add an equal sign to an expression, it becomes an equation.
For example, 2x=14{\displaystyle 2x=14} is an equation. -
Step 2: Understand what a variable is.
A variable is a symbol, usually a letter, that stands for an unknown value.In algebra, you are usually trying to find the value of the variable.
In order to evaluate an algebraic expression, however, you need to be given the variable’s value. , Evaluate means to simplify an expression.
When you are asked to evaluate an algebraic expression, you need to plug a given value for the variable into the expression and solve.For example, you might be asked to evaluate 2x{\displaystyle 2x} when x=2{\displaystyle x=2}. , This information should be given to you.
Usually you will be told to evaluate the expression “when” or “where” the variable is equal to a certain value.
If you are not given the variable’s value, you cannot evaluate the expression.
For example, you might be asked to evaluate the expression 5x−10{\displaystyle 5x-10} when x=8{\displaystyle x=8}. , To do this, plug the given value into the expression wherever you see the variable.
If the variable has a coefficient (a number you need to multiply its value by), make sure to put the value in parentheses.
For example, to evaluate 5x−10{\displaystyle 5x-10} when x=8{\displaystyle x=8}, replace the x{\displaystyle x} in the equation with 8{\displaystyle 8}: 5(8)−10{\displaystyle 5(8)-10}. , Remember to follow the order of operations when solving an expression.
When you complete your calculations rewrite the expression as an equation.
For example:5(8)−10{\displaystyle 5(8)-10}=40−10{\displaystyle =40-10}=30{\displaystyle =30}So, 5(8)−10=30{\displaystyle 5(8)-10=30}. , To do this, follow the same steps as you do for evaluating an expression with one variable, except plug in the values for both variables into the equation.
These values should be given.
Make sure you do not switch the values.
The x{\displaystyle x} value cannot be substituted for the y{\displaystyle y} variable and vice versa.
Doing so will give you an incorrect solution. , Identify the variable and its value.
The variable is x{\displaystyle x}, and you are evaluating the expression for x=3{\displaystyle x=3}.
Substitute the given value for the variable: 2(3)+3{\displaystyle 2(3)+3}.
Make the necessary calculations: 2(3)+3=6+3=9{\displaystyle 2(3)+3=6+3=9}.
Write the equation: 2(3)+3=9{\displaystyle 2(3)+3=9} , Identify both variables and their values.
The variables are x{\displaystyle x} and y{\displaystyle y}, and you are evaluating the expression for x=2{\displaystyle x=2} and y=6{\displaystyle y=6}.
Substitute both given values for the variables: 4(2)+3(6){\displaystyle 4(2)+3(6)}.
Make the necessary calculations: 4(2)+3(6)=8+18=26{\displaystyle 4(2)+3(6)=8+18=26}.
Write the equation: 4(2)+3(6)=26{\displaystyle 4(2)+3(6)=26}. , Identify the variable and its value.
The variable is x{\displaystyle x}, and you are evaluating the expression for x=4{\displaystyle x=4}.
Substitute the given value for the variable: 7(4)2−12(4)+13{\displaystyle 7(4)^{2}-12(4)+13}.
Make the necessary calculations.
Remember when working with exponents that you should calculate the exponent before multiplying by a coefficient:7(4)2−12(4)+13{\displaystyle 7(4)^{2}-12(4)+13}=7(16)−12(4)+13{\displaystyle =7(16)-12(4)+13}=112−48+13{\displaystyle =112-48+13}=64+13{\displaystyle =64+13}=77{\displaystyle =77} Write the equation: 7(16)−12(4)+13=77{\displaystyle 7(16)-12(4)+13=77} -
Step 3: Determine how to evaluate the expression.
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Step 4: Identify the variable and its value.
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Step 5: Substitute the given value for the variable.
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Step 6: Complete the necessary calculations.
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Step 7: Evaluate an expression with Two Variables.
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Step 8: Evaluate the following expression when x=3{\displaystyle x=3}: 2x+3{\displaystyle 2x+3}.
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Step 9: Evaluate the following expression with two variables when x=2{\displaystyle x=2} and y=6{\displaystyle y=6}: 4x+3y{\displaystyle 4x+3y}.
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Step 10: Evaluate the following polynomial when x=4{\displaystyle x=4}: 7x2−12x+13{\displaystyle 7x^{2}-12x+13}.
Detailed Guide
An algebraic expression is a set of numbers and letters combined by mathematical operations, such as addition, subtraction, division, and multiplication.
The numbers in the expression are called constants or coefficients, depending on their function.
The letters are called variables.2x{\displaystyle 2x} is an expression.
In this expression, you are multiplying the coefficient 2{\displaystyle 2} by the variable x{\displaystyle x}. 2x+3y{\displaystyle 2x+3y} is an expression called a binomial.
In this expression, you add the product of 3y{\displaystyle 3y} to the product of 2x{\displaystyle 2x}.
In this expression, 2{\displaystyle 2} and 3{\displaystyle 3} are coefficients, and x{\displaystyle x} and y{\displaystyle y} are variables.
Once you add an equal sign to an expression, it becomes an equation.
For example, 2x=14{\displaystyle 2x=14} is an equation.
A variable is a symbol, usually a letter, that stands for an unknown value.In algebra, you are usually trying to find the value of the variable.
In order to evaluate an algebraic expression, however, you need to be given the variable’s value. , Evaluate means to simplify an expression.
When you are asked to evaluate an algebraic expression, you need to plug a given value for the variable into the expression and solve.For example, you might be asked to evaluate 2x{\displaystyle 2x} when x=2{\displaystyle x=2}. , This information should be given to you.
Usually you will be told to evaluate the expression “when” or “where” the variable is equal to a certain value.
If you are not given the variable’s value, you cannot evaluate the expression.
For example, you might be asked to evaluate the expression 5x−10{\displaystyle 5x-10} when x=8{\displaystyle x=8}. , To do this, plug the given value into the expression wherever you see the variable.
If the variable has a coefficient (a number you need to multiply its value by), make sure to put the value in parentheses.
For example, to evaluate 5x−10{\displaystyle 5x-10} when x=8{\displaystyle x=8}, replace the x{\displaystyle x} in the equation with 8{\displaystyle 8}: 5(8)−10{\displaystyle 5(8)-10}. , Remember to follow the order of operations when solving an expression.
When you complete your calculations rewrite the expression as an equation.
For example:5(8)−10{\displaystyle 5(8)-10}=40−10{\displaystyle =40-10}=30{\displaystyle =30}So, 5(8)−10=30{\displaystyle 5(8)-10=30}. , To do this, follow the same steps as you do for evaluating an expression with one variable, except plug in the values for both variables into the equation.
These values should be given.
Make sure you do not switch the values.
The x{\displaystyle x} value cannot be substituted for the y{\displaystyle y} variable and vice versa.
Doing so will give you an incorrect solution. , Identify the variable and its value.
The variable is x{\displaystyle x}, and you are evaluating the expression for x=3{\displaystyle x=3}.
Substitute the given value for the variable: 2(3)+3{\displaystyle 2(3)+3}.
Make the necessary calculations: 2(3)+3=6+3=9{\displaystyle 2(3)+3=6+3=9}.
Write the equation: 2(3)+3=9{\displaystyle 2(3)+3=9} , Identify both variables and their values.
The variables are x{\displaystyle x} and y{\displaystyle y}, and you are evaluating the expression for x=2{\displaystyle x=2} and y=6{\displaystyle y=6}.
Substitute both given values for the variables: 4(2)+3(6){\displaystyle 4(2)+3(6)}.
Make the necessary calculations: 4(2)+3(6)=8+18=26{\displaystyle 4(2)+3(6)=8+18=26}.
Write the equation: 4(2)+3(6)=26{\displaystyle 4(2)+3(6)=26}. , Identify the variable and its value.
The variable is x{\displaystyle x}, and you are evaluating the expression for x=4{\displaystyle x=4}.
Substitute the given value for the variable: 7(4)2−12(4)+13{\displaystyle 7(4)^{2}-12(4)+13}.
Make the necessary calculations.
Remember when working with exponents that you should calculate the exponent before multiplying by a coefficient:7(4)2−12(4)+13{\displaystyle 7(4)^{2}-12(4)+13}=7(16)−12(4)+13{\displaystyle =7(16)-12(4)+13}=112−48+13{\displaystyle =112-48+13}=64+13{\displaystyle =64+13}=77{\displaystyle =77} Write the equation: 7(16)−12(4)+13=77{\displaystyle 7(16)-12(4)+13=77}
About the Author
Douglas Henderson
Creates helpful guides on lifestyle to inspire and educate readers.
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