Hint: We will first write the definition of algebraic expression and see if the given expression $x + 1$ falls into the category by following all the requirements or not.
Complete step-by-step answer:
Let us first write the definition of Algebraic expressions:
Algebraic Expressions: The combination of constants and variables, connected by signs of fundamental operations $( + , - , \times , \div )$is called an algebraic expression.
It has two terms “constants” and “variable” which can create confusion to be understood.
Let us decipher those terms as well.
Constants: A quantity or parameter that does not change its value whatever the value of the variables, under a given set of conditions is known as constant.
Here, we have 1 as a constant.
Variables: A quantity which is not consistent or having a fixed pattern that means liable to change is known as a variable.
Here, we have $x$ as a variable.
These both things are combined by the fundamental operation ‘+’.
Hence, it satisfies all the things to be an algebraic expression.
Hence, the statement is true.
Note: We must read the question carefully because we might mistakenly or hurriedly miss out of some important word in the question. For example:- If the question would have been given as follows:
State whether the statement given below is true or not:
The expression $x + 1$ is not an algebraic expression.
Then, according to the arguments we used, our answer would have been false.
Always remember the definitions of Algebraic Expression, Variables and Constants.
Variables can be in different forms as well, like we can have variables with powers and coefficients.
Then, treat coefficients as a constant fused with variables by the fundamental operation ‘$ \times $’ and power will come under variable part only.