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

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.

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

Examples with solutions for The Domain of an Algebraic Expression

Exercise #1

What will be the result of this algebraic expression:

5x6 5x-6

if we place

x=0 x=0

Video Solution

Step-by-Step Solution

Usually we don't know the value of the unknown and need to find it,

However, in this case they give us a value, so the first action will be to substitute it into the expression,

Meaning, replace every place where X is written with 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:

5x6 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

156=21 -15-6=-21

Answer

21 -21

Exercise #3

What will be the result of this algebraic expression:

8ab(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 #4

What will be the result of this algebraic expression:

5x6 5x-6

if we place

x=8 x=8

Video Solution

Answer

34

Exercise #5

What will be the result of this algebraic expression:

5x6 5x-6

if we place

x=2 x=-2

Video Solution

Answer

16 -16

Exercise #6

What will be the result of this algebraic expression:

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

if we place

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

Video Solution

Answer

13 13

Exercise #7

What will be the result of this algebraic expression:

8(x7)+4(62y) 8(x-7)+4(6-2y)

if we place

x=0,y=1 x=0,y=-1

Video Solution

Answer

24 -24

Exercise #8

What will be the result of this algebraic expression:

8(x7)+4(62y) 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:

8ab(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=5 x=5 .

XXX

Video Solution

Answer

60 60

Exercise #11

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

8X8X8XXXX

Video Solution

Answer

36 36

Exercise #12

What will be the result of this algebraic expression:

8(x7)+4(62y) 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