Evaluating Variables and Expressions

In this article, we will teach you how to evaluate an expression that has variables.

Evaluating Variables and Expressions

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 a letter, for instance, \(x, y\) or \(z\), which signifies 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.

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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, switch each variable with the assigned value, then simplify the expression like before.

Evaluating Variables – Example 1:

Simplify. \(a-1, a=4\)


We place the value of the variable in the expression: \(a-1=4-1=3\)

Evaluating Variables – Example 2:

Simplify. \(2x+y, x=2, y=3\)


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.

  • \(\color{blue}{x + 3y – 1, \\ x = 1, y = 3 } \\\)
  • \(\color{blue}{3a – 4, \\ a = 4} \\ \)
  • \(\color{blue}{5 + 5x – y, \\ x = 1, y = 3} \\ \)
  • \(\color{blue}{x + 15, \\ x = 10} \\ \)
  • \(\color{blue}{2 – 2x +y, \\ x = 7, y = 2} \\ \)
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  • \(\color{blue}{9}\)
  • \(\color{blue}{8}\)
  • \(\color{blue}{7}\)
  • \(\color{blue}{25}\)
  • \(\color{blue}{14}\)

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