Indicate which are valid expressions. $x$ and $y$ are variables.
1) $x+1$
Valid
Not valid
2) 2 * $(x-y)$
Valid
Not valid
3) $x$
Valid
Not valid
4) 2
Valid
Not valid
5) $2 x$
Valid
Not valid
6) $2+(x y)$
Valid
Not valid
7) $y=x+1$
Valid
Answer (1)
x + 1 is a valid expression.
2 ∗ ( x − y ) is a valid expression.
x is a valid expression.
2 is a valid expression.
2 x is a valid expression.
2 + ( x y ) is a valid expression.
y = x + 1 is not a valid expression.
Explanation
Understanding Valid Expressions We need to determine which of the given options are valid mathematical expressions, given that x and y are variables. A valid expression is something that can be evaluated to a numerical value if we substitute numbers for the variables. An equation, on the other hand, states a relationship between expressions and is not an expression itself.
Analyzing Option 1
x + 1 : This is a valid expression because it represents the sum of a variable and a constant. If we substitute a value for x , we can evaluate the expression.
Analyzing Option 2
2 ∗ ( x − y ) : This is a valid expression because it represents the product of a constant and the difference of two variables. If we substitute values for x and y , we can evaluate the expression.
Analyzing Option 3
x : This is a valid expression because it represents a variable. If we substitute a value for x , we can evaluate the expression.
Analyzing Option 4
2 : This is a valid expression because it represents a constant. It is already a numerical value.
Analyzing Option 5
2 x : This is a valid expression because it represents the product of a constant and a variable. If we substitute a value for x , we can evaluate the expression.
Analyzing Option 6
2 + ( x y ) : This is a valid expression because it represents the sum of a constant and the product of two variables. If we substitute values for x and y , we can evaluate the expression.
Analyzing Option 7
y = x + 1 : This is not a valid expression because it is an equation, not an expression. It states a relationship between y and x , but it doesn't represent a value that can be calculated directly from given values of x and y .
Examples
In programming, understanding valid expressions is crucial for writing code that the computer can understand and execute. For example, if you want to calculate the area of a rectangle, you would use the expression l e n g t h ∗ w i d t h . Similarly, if you want to calculate the total cost of items with tax, you would use the expression p r i ce + ( p r i ce ∗ t a x R a t e ) . These expressions allow the computer to perform calculations and produce meaningful results. Equations, on the other hand, are used to define relationships between variables or to set conditions for certain actions.
