The Domain of an Algebraic Expression - Examples, Exercises and Solutions

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

What will be the result of this algebraic expression:

\( 8(x-7)+4(6-2y) \)

if we place

\( x=7.1,y=\frac{5}{8} \)

Examples with solutions for The Domain of an Algebraic Expression

Step-by-step solutions included
Exercise #1

Solve the algebraic expression 5x6 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:

5x6 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:

5x6 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

156=21 -15-6=-21

Answer:

21 -21

Video Solution
Exercise #4

What will be the result of this algebraic expression:

5x6 5x-6

if we place

x=2 x=-2

Step-by-Step Solution

To solve this problem, we will evaluate the algebraic expression 5x6 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 5x6 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:

106 -10 - 6

  • Step 4: Now perform the subtraction:

106=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:

8ab(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

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