Question

State whether \[2n+1=11\] is an equation(with a variable) or not. Give reason and tell your answer. Identify the variable from the equation.

Answer 1

Hint: We will use the definition of equation to solve this problem. An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Complete step-by-step answer:
Before proceeding with the question we should understand the definition of equations.
The equation is an expression where two sides of the expression are connected through an equal to sign (=). \[2x+8=9\] is an equation, where 2x+8 is the left-hand side (LHS) and 9 is the right-hand side (RHS) of the expression. The equal sign between LHS and RHS indicates that the value of LHS is equal to the RHS of the expression. \[11x+69>13\], is not an equation. Here, the sign between LHS and RHS of the expression is not an equal sign. Hence, we can say every expression is not an equation.
So from the above definition \[2n+1=11\] is an equation because here in this equation n is a variable and 2n+1 is the left hand side of the equation and 11 is the right hand side of the equation and there is an equal sign between L.H.S and R.H.S. We can also find the value of n because the left hand side of the equation is equal to the right hand side of the equation.
\[2n+1=11.......(1)\]
Separate the variable and the constant term: Keep variable term on the left-hand side, and move the constant term on the right-hand side.
\[\begin{align}
  & 2n=11-1 \\
 & 2n=10 \\
 & n=\dfrac{10}{2}=5 \\
\end{align}\]
Hence \[2n+1=11\] is an equation.

Note: An equation is interchangeable i.e. the equation remains the same even if LHS and RHS interchange each other. Whenever there will be any symbol other than equal to ‘’=’’ then it will not be called an equation.