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

Question Types:
The Domain of an Algebraic Expression: Only addition and subtractionThe Domain of an Algebraic Expression: More than one unknown

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

Suggested Topics to Practice in Advance

  1. Variables in Algebraic Expressions
  2. Equivalent Expressions
  3. Multiplication of Algebraic Expressions
  4. Simplifying Expressions (Collecting Like Terms)

Practice The Domain of an Algebraic Expression

Question 1

Solve the algebraic expression \( 5x-6 \) given that \( x=0 \).

Question 2

What will be the result of this algebraic expression:

\( 5x-6 \)

if we place

\( x=8 \)

Question 3

What will be the result of this algebraic expression:

\( 5x-6 \)

if we place

\( x=-3 \)

Question 4

What will be the result of this algebraic expression:

\( 8a-b(7+a) \)

if we ascertain that:

\( a=50,b=0 \)

Question 5

What will be the result of this algebraic expression:

\( 8a-b(7+a) \)

if we place

\( a=2,b=\frac{1}{3} \)

Examples with solutions for The Domain of an Algebraic Expression

Exercise #1

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

Video Solution

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

Exercise #2

What will be the result of this algebraic expression:

5x−6 5x-6

if we place

x=8 x=8

Video Solution

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

Exercise #3

What will be the result of this algebraic expression:

5x−6 5x-6

if we place

x=−3 x=-3

Video Solution

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

Exercise #4

What will be the result of this algebraic expression:

8a−b(7+a) 8a-b(7+a)

if we ascertain that:

a=50,b=0 a=50,b=0

Video Solution

Step-by-Step Solution

Let's insert the given data into the expression:

8*50-0(7+50) =
400-0*57 =
400-0 =
400

Answer

400 400

Exercise #5

What will be the result of this algebraic expression:

8a−b(7+a) 8a-b(7+a)

if we place

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

Video Solution

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

Question 1

What will be the result of this algebraic expression:

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

if we place

\( x=0,y=-1 \)

Question 2

What will be the result of this algebraic expression:

\( 5x-6 \)

if we place

\( x=-2 \)

Question 3

What will be the result of this algebraic expression:

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

if we place

\( x=8,y=5 \)

Question 4

What will be the result of this algebraic expression:

\( 8a-b(7+a) \)
if we place

\( a=-\frac{1}{2},b=\frac{2}{13} \)

Question 5

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

8X8X8XXXX

Exercise #6

What will be the result of this algebraic expression:

8(x−7)+4(6−2y) 8(x-7)+4(6-2y)

if we place

x=0,y=−1 x=0,y=-1

Video Solution

Step-by-Step Solution

We have the given exercise, and it has two variables, X and Y.

In this case, we are given the values of these variables,

Therefore, what we need to do is substitute them in the relevant place in the exercise:

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

We know that x=0, so we will replace every X in the exercise with 0:

8(0-7)+4(6-2y)=
8(-7)+4(6-2y)=
-56+4(6-2y)=

We'll do the same thing with y, knowing that it equals -1

-56+4(6-2*(-1))=
-56+4(6-(-2)))=

-56+4(8)=

-56+32=

-24

And that's the solution!

Answer

−24 -24

Exercise #7

What will be the result of this algebraic expression:

5x−6 5x-6

if we place

x=−2 x=-2

Video Solution

Answer

−16 -16

Exercise #8

What will be the result of this algebraic expression:

8(x−7)+4(6−2y) 8(x-7)+4(6-2y)

if we place

x=8,y=5 x=8,y=5

Video Solution

Answer

−8 -8

Exercise #9

What will be the result of this algebraic expression:

8a−b(7+a) 8a-b(7+a)
if we place

a=−12,b=213 a=-\frac{1}{2},b=\frac{2}{13}

Video Solution

Answer

−5 -5

Exercise #10

Calculate the perimeter of the rectangle given that x=2 x=2 .

8X8X8XXXX

Video Solution

Answer

36 36

Question 1

Calculate the perimeter of the rectangle given that \( x=5 \).

XXX

Question 2

What will be the result of this algebraic expression:

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

if we place

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

Exercise #11

Calculate the perimeter of the rectangle given that x=5 x=5 .

XXX

Video Solution

Answer

60 60

Exercise #12

What will be the result of this algebraic expression:

8(x−7)+4(6−2y) 8(x-7)+4(6-2y)

if we place

x=7.1,y=58 x=7.1,y=\frac{5}{8}

Video Solution

Answer

19.8 19.8

Topics learned in later sections

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