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

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

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

Practice The Domain of an Algebraic Expression

Question 1

What will be the result of this algebraic expression:

$$ 5x-6 $$

if we place

$$ x=0 $$

Question 2

What will be the result of this algebraic expression:

$$ 5x-6 $$

if we place

$$ x=-3 $$

Question 3

What will be the result of this algebraic expression:

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

if we ascertain that:

$$ a=50,b=0 $$

Question 4

What will be the result of this algebraic expression:

$$ 5x-6 $$

if we place

$$ x=8 $$

Question 5

What will be the result of this algebraic expression:

$$ 5x-6 $$

if we place

$$ x=-2 $$

Examples with solutions for The Domain of an Algebraic Expression

Exercise #1

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=0$

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

$-6$

Exercise #2

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=-3$

Video Solution

Step-by-Step Solution

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

$5(-3)-6$

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.

$5\times-3=-15$

$-15-6=-21$

Answer

$-21$

Exercise #3

What will be the result of this algebraic expression:

$8a-b(7+a)$

if we ascertain that:

$a=50,b=0$

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

$400$

Exercise #4

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=8$

Video Solution

Answer

Exercise #5

What will be the result of this algebraic expression:

$5x-6$

if we place

$x=-2$

Video Solution

Answer

$-16$

Question 1

What will be the result of this algebraic expression:

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

if we place

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

Question 2

What will be the result of this algebraic expression:

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

if we place

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

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 $$ x=2 $$ .

Exercise #6

What will be the result of this algebraic expression:

$8a-b(7+a)$

if we place

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

Video Solution

Answer

$13$

Exercise #7

What will be the result of this algebraic expression:

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

if we place

$x=0,y=-1$

Video Solution

Answer

$-24$

Exercise #8

What will be the result of this algebraic expression:

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

if we place

$x=8,y=5$

Video Solution

Answer

$-8$

Exercise #9

What will be the result of this algebraic expression:

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

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

Video Solution

Answer

$-5$

Exercise #10

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

Video Solution

Answer

$36$

Question 1

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

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 $x=5$ .

Video Solution

Answer

$60$

Exercise #12

What will be the result of this algebraic expression:

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

if we place

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

Video Solution

Answer

$19.8$

Topics learned in later sections

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

Suggested Topics to Practice in Advance

Practice The Domain of an Algebraic Expression

Examples with solutions for The Domain of an Algebraic Expression

Exercise #1

Video Solution

Step-by-Step Solution

Answer

Exercise #2

Video Solution

Step-by-Step Solution

Answer

Exercise #3

Video Solution

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Answer

Exercise #5

Video Solution

Answer

Exercise #6

Video Solution

Answer

Exercise #7

Video Solution

Answer

Exercise #8

Video Solution

Answer

Exercise #9

Video Solution

Answer

Exercise #10

Video Solution

Answer

Exercise #11

Video Solution

Answer

Exercise #12

Video Solution

Answer

Topics learned in later sections