Question

If value of \[x\] exceeds 3 by 7 , can be represented as
A.\[x + 3 = 2\]
B.\[x + 7 = 3\]
C.\[x - 3 = 7\]
D.\[x - 7 = 3\]

Answer 1

Hint: Here, the given problem should be represented in the form of an algebraic equation. An algebraic equation is a combination of constants and variables combined together with the help of the four fundamental signs.

Complete step-by-step answer:
Algebraic expressions are expressions made up of variables and constants along with mathematical operators.
The given statement with give has a linear equation in one variable.
A linear equation with one variable is an equation which can be written in the form of \[ax + b = 0\] where \[x\] is the variable and \[a\] and \[b\] are the two integers. Since, this is a linear equation, hence the variable \[x\] will always have a power 1. This is because, if the power of \[x\]will become 2 then it would become a quadratic equation and so on.
And since, this is a linear equation with one variable, hence, there would be a single variable \[x\], having a single solution.
Now, if we try to understand carefully by breaking this sentence, then it is trying to state that:
The variable \[x\]exceeds 3, i.e.
The variable \[x\] is ‘greater than’ 3
Hence, here, \[x > 3\]
Now, the complete sentence states that:
\[x\] exceeds 3 by 7.
\[ \Rightarrow x\] is greater than 3 by 7
\[ \Rightarrow x > 3\] by 7
Hence, since, \[x\] is greater than 3 by 7, we can say that if we ‘subtract’ 3 from the variable \[x\] , we would get the answer 7
\[ \Rightarrow x - 3 = 7\]
Therefore, option C is the correct answer.

Note: There are three main types of algebraic expressions, by the position of variables, the types of functions and operations, and the behavior of their graphs. The algebraic expression consisting of just one term is known as Monomial expressions. The algebraic equation consisting of two unlikely terms are considered as Binomial expressions. A polynomial expression is considered the ones which consist of more than one term with non-negative integral exponents of a variable.