Evaluating Variables and Expressions

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

Tutor-style math help

Evaluating Variables and Expressions: what to notice and how to work it

Expressions skill

Expression problems ask you to translate, simplify, or evaluate. The safest approach is to turn words into symbols one phrase at a time.

What to notice first

Underline the quantity being changed, then attach the operation to that quantity. Phrases like 'less than' and 'quotient of' are order-sensitive.

Common student mistake

Do not reverse subtraction. '5 less than x' means \(x-5\), because x is the amount being reduced.

Key formulas and cues

\(\text{twice }x=2x\)

\(\text{5 less than }x=x-5\)

\(\text{evaluate means substitute first}\)

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

Example: Seven more than twice a number

Let the number be x.
Twice the number is 2x.
Seven more than that adds 7.

Answer: \(2x+7\)

Evaluate carefully

Example: \(3x-4\) when \(x=5\)

Replace x with 5.
Multiply before subtracting.
Compute 15 – 4.

Answer: \(11\)

Open pop-up practice

Try one before moving on

Try: Write 'three less than four times a number.'

Answer: \(4x-3\).

Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

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.

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

\(\color{blue}{9}\)
\(\color{blue}{8}\)
\(\color{blue}{7}\)
\(\color{blue}{25}\)
\(\color{blue}{14}\)

Effortless Math Team

38 minutes ago

Effortless Math Team

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Evaluating Variables and Expressions