Introduction to variable expressions:
Expressions with variables are obtained by operations of addition, subtraction, multiplication and division on variables. For example, the expression 2n is formed by multiplying the variable n by 2; the expression (x + 10) is formed by adding 10 to the variable x and so on.
We know that variables can take different values; they have no fixed value. But they are nothing but numbers. That is why as in the case of numbers, arithmetic operations like addition, subtraction, multiplication and division can be done on them.
Simple Variable Expressions and their Formation
One important point must be noted regarding the expressions containing variables. A number expression like (4 × 3) + 5 can be immediately evaluated as (4 × 3) + 5 = 12 + 5 = 17.
But an expression like (4x + 5), which contains the variable x, cannot be evaluated. Only if x is given some value, an expression like (4x + 5) can be evaluated. For example, when x = 3, 4x + 5 = (4 × 3) + 5 = 17 as found above.
Formation of Variable Expressions
y + 5 5 added to y
t – 7 7 subtracted from t
3 x + 2 first x multiplied by 3, then 2 added to the product
10 a a multiplied by 10
x / 3 x divided by 3
– 5 q q multiplied by –5
2 y – 5 first y multiplied by 2, then 5 subtracted from the product
10y+7 y multiplied by 10 and then 7 added to the product
2n-1 n multiplied by 2 and 1 subtracted from the product
Stuck on any of these topics Compound Inequalities Word Problems, Solving Linear Equations and Inequalities try out some best online tutoring math website.
Evaluating Variable Expressions
Example 1: Evaluate the variable expressions.
x+2y;
x=2, y=3
Solution:
Substitute the x, y and z values in the given expression.
x+2y=2+2(3)
=2+6
=8
Example 2: Evaluate the variable expressions.
(x + y)/x y;
x=7, y=6
Solution:
(x + y)/x y= (7+6) / (7*6)
= 13/42
Example 3: Evaluate the expressions.
7xy+5yz+3zx-40;
x=-1, y=1, z=-3
Solution:
7xy+5yz+3zx-40=7(-1) (1) +5(1) (-3) +3(-3) (-1)-40
= (-7) + (-15) + (9) – 40
=-7-15+9-40
=-53
Example 4: Evaluate the expressions.
(2x+y+z)-(x+y-2z); x=8, y=7, z= 4
Solution:
(2x+y+z)-(x+y-2z) = (2(8) + (7) + 4)-((8) + 7-2(4))
= (16+7+4)-(8+7-8)
= 27-7
= 20
Example 5: Evaluate the variable expressions.
(x+1) + (y+1) + (z+1)-(z-1);
x=6, y=7, b z=3
Solution:
(x+1) + (y+1) + (z+1)-(z-1) = (6+1) + (7+1) + (3+1)-(3-1)
= 7+8+4-2
= 17
Expressions with variables are obtained by operations of addition, subtraction, multiplication and division on variables. For example, the expression 2n is formed by multiplying the variable n by 2; the expression (x + 10) is formed by adding 10 to the variable x and so on.
We know that variables can take different values; they have no fixed value. But they are nothing but numbers. That is why as in the case of numbers, arithmetic operations like addition, subtraction, multiplication and division can be done on them.
Simple Variable Expressions and their Formation
One important point must be noted regarding the expressions containing variables. A number expression like (4 × 3) + 5 can be immediately evaluated as (4 × 3) + 5 = 12 + 5 = 17.
But an expression like (4x + 5), which contains the variable x, cannot be evaluated. Only if x is given some value, an expression like (4x + 5) can be evaluated. For example, when x = 3, 4x + 5 = (4 × 3) + 5 = 17 as found above.
Formation of Variable Expressions
y + 5 5 added to y
t – 7 7 subtracted from t
3 x + 2 first x multiplied by 3, then 2 added to the product
10 a a multiplied by 10
x / 3 x divided by 3
– 5 q q multiplied by –5
2 y – 5 first y multiplied by 2, then 5 subtracted from the product
10y+7 y multiplied by 10 and then 7 added to the product
2n-1 n multiplied by 2 and 1 subtracted from the product
Stuck on any of these topics Compound Inequalities Word Problems, Solving Linear Equations and Inequalities try out some best online tutoring math website.
Evaluating Variable Expressions
Example 1: Evaluate the variable expressions.
x+2y;
x=2, y=3
Solution:
Substitute the x, y and z values in the given expression.
x+2y=2+2(3)
=2+6
=8
Example 2: Evaluate the variable expressions.
(x + y)/x y;
x=7, y=6
Solution:
(x + y)/x y= (7+6) / (7*6)
= 13/42
Example 3: Evaluate the expressions.
7xy+5yz+3zx-40;
x=-1, y=1, z=-3
Solution:
7xy+5yz+3zx-40=7(-1) (1) +5(1) (-3) +3(-3) (-1)-40
= (-7) + (-15) + (9) – 40
=-7-15+9-40
=-53
Example 4: Evaluate the expressions.
(2x+y+z)-(x+y-2z); x=8, y=7, z= 4
Solution:
(2x+y+z)-(x+y-2z) = (2(8) + (7) + 4)-((8) + 7-2(4))
= (16+7+4)-(8+7-8)
= 27-7
= 20
Example 5: Evaluate the variable expressions.
(x+1) + (y+1) + (z+1)-(z-1);
x=6, y=7, b z=3
Solution:
(x+1) + (y+1) + (z+1)-(z-1) = (6+1) + (7+1) + (3+1)-(3-1)
= 7+8+4-2
= 17
