Domain of Algebraic Expressions Practice Problems

Master finding numerical values of algebraic expressions with step-by-step practice problems. Learn to substitute variables and solve complex expressions confidently.

📚What You'll Practice in This Section
  • Substitute given values for variables in algebraic expressions
  • Calculate numerical values of expressions with multiple variables
  • Solve complex expressions involving fractions, exponents, and operations
  • Apply order of operations when evaluating algebraic expressions
  • Work with expressions containing the same variable multiple times
  • Master substitution techniques for single and multi-variable expressions

Understanding The Domain of an Algebraic Expression

Complete explanation with examples

An algebraic expression is a combination of constant numbers (or 'integers'), unknown variables represented by letters, and basic operations. When we assign numerical values to each of the unknown variables, we can reduce the expression to a numerical value.

If you are unsure about these terms, you can click on the link for more information about variables in algebraic expressions.

For example:

If we take the algebraic expression X+5 X+5 and assign the variable X X a value equal to 3 3 , then the value of the algebraic expression will be 8 8 .

  • Algebraic expression:
    X+5 X+5
  • Algebraic expression after having given the variable X X a value of 3 3 :
    5+3 5+3
  • Therefore, the value (result) of the algebraic expression is 8 8 :
    5+3=8 5+3=8

If the same variable appears several times in an algebraic expression, each has the same numerical value.

Detailed explanation

Practice The Domain of an Algebraic Expression

Test your knowledge with 2 quizzes

Calculate the perimeter of the rectangle given that \( x=2 \).

8X8X8XXXX

Examples with solutions for The Domain of an Algebraic Expression

Step-by-step solutions included
Exercise #1

Solve the algebraic expression 5x−6 5x-6 given that x=0 x=0 .

Step-by-Step Solution

Usually we do not know the value of the unknown variable and need to work it out.

However, in this case we know its value and so the first thing we will do is substitute it into the expression—that is, replace each x x with the value 0.

5*0-6=
0-6=-6

Therefore, the result is -6.

Answer:

−6 -6

Video Solution
Exercise #2

What will be the result of this algebraic expression:

5x−6 5x-6

if we place

x=8 x=8

Step-by-Step Solution

To answer the question we first need to understand what X is.

X is an unknown, meaning it's a symbol that represents another number, an unknown one, that could be there in its place.

Usually in exercises we'll need to calculate and discover what X is appropriate for each exercise,

but in this case the result is given to us: X=8
Therefore, we can substitute (plug in) the value 8 everywhere X appears in the exercise.

 

So we get:

5*8-6

40-6
34

 

Answer:

34

Video Solution
Exercise #3

What will be the result of this algebraic expression:

5x−6 5x-6

if we place

x=−3 x=-3

Step-by-Step Solution

The first step is to substitute X in the exercise, resulting in:

5(−3)−6 5(-3)-6

When we have two numbers with different signs, meaning one number is negative and the other is positive or vice versa,

the result of multiplication or division will always be negative.

5×−3=−15 5\times-3=-15

−15−6=−21 -15-6=-21

Answer:

−21 -21

Video Solution
Exercise #4

What will be the result of this algebraic expression:

5x−6 5x-6

if we place

x=−2 x=-2

Step-by-Step Solution

To solve this problem, we will evaluate the algebraic expression 5x−6 5x - 6 by substituting the value of x=−2 x = -2 into it.

Step-by-step solution:

  • Step 1: Substitute x=−2 x = -2 into the expression 5x−6 5x - 6 . This gives:

5(−2)−6 5(-2) - 6

  • Step 2: Perform the operations in the expression. Start with the multiplication:

5(−2)=−10 5(-2) = -10

  • Step 3: Substitute the result of the multiplication back into the expression:

−10−6 -10 - 6

  • Step 4: Now perform the subtraction:

−10−6=−16 -10 - 6 = -16

Therefore, the result of the expression when x=−2 x = -2 is −16 -16 .

Comparing this result with the given choices, we conclude that the correct choice is:

−16 -16

Answer:

−16 -16

Video Solution
Exercise #5

Solve the following expression:

8a−b(7+a) 8a-b(7+a)

If

a=2,b=13 a=2,b=\frac{1}{3}

Step-by-Step Solution

Note that we have two unknowns, a and b, and we are also given values for them,

Therefore, let's start by substituting these values in the equation instead of the unknowns:

8*2-1/3*(7+2)=

When there is a number before parentheses, it's like having a multiplication sign between them.

Let's start solving according to the order of operations, beginning with the parentheses:

8*2-1/3*(9)=

Now let's continue with multiplication and division:

16-9/3=
16-3=

‎‎‎‎‎‎‎13

And that's the solution!

Answer:

13 13

Video Solution

Frequently Asked Questions

Everything you need to know about The Domain of an Algebraic Expression

What is the domain of an algebraic expression?

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The domain of an algebraic expression is the set of all possible values that can be assigned to the variables in the expression. It represents all valid input values that make the expression mathematically meaningful and avoid undefined operations like division by zero.

How do you find the numerical value of an algebraic expression?

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To find the numerical value: 1) Substitute the given values for each variable, 2) Replace all variables with their assigned numbers, 3) Follow the order of operations (PEMDAS) to calculate the final result. For example, if X=3 in the expression X+5, substitute to get 3+5=8.

What happens when the same variable appears multiple times in an expression?

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When the same variable appears multiple times, each occurrence gets the same numerical value. For example, in X+5-X where X=3, both X's become 3, giving us 3+5-3=5.

Can algebraic expressions have decimal values for variables?

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Yes, variables in algebraic expressions can be assigned decimal values. For instance, if X=2.5 in the expression (X+X)3/3, we substitute to get (2.5+2.5)3/3 = (5)3/3 = 15/3 = 5.

What are common mistakes when evaluating algebraic expressions?

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Common mistakes include: • Forgetting to substitute all instances of a variable • Not following the correct order of operations • Making arithmetic errors during calculation • Confusing different variables (like X and Y) • Not properly handling negative signs when substituting

How do you work with fractions in algebraic expressions?

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When working with fractions: 1) Substitute variable values into both numerator and denominator, 2) Simplify each part separately, 3) Perform the division or reduce to lowest terms. For example, with X/6 + Y/6 where X=12 and Y=9, you get 12/6 + 9/6 = 2 + 1.5 = 3.5.

Why is finding numerical values of expressions important?

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Finding numerical values helps solve real-world problems by converting abstract algebraic relationships into concrete numbers. This skill is essential for physics formulas, engineering calculations, financial computations, and understanding how mathematical models apply to practical situations.

What should I do if I get confused while substituting variables?

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If confused: • Write out each step clearly • Use parentheses when substituting to avoid sign errors • Check your arithmetic at each step • Practice with simpler expressions first • Ask for help from teachers or tutors when needed, as building strong foundations prevents future struggles

Continue Your Math Journey

Master The Domain of an Algebraic Expression first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

Variables in Algebraic ExpressionsEquivalent ExpressionsMultiplication of Algebraic ExpressionsSimplifying Expressions (Collecting Like Terms)

Topics Learned in Later Sections

Transposition of terms and domain of equations of one unknown.Domain of a Function

Practice by Question Type

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More than one unknown Only addition and subtraction