Question

Construct 3 equations starting with $x=2$.

Answer 1

Hint:We have to start with $x=2$, so initially our LHS is equal to $''x''$and RHS is equal to “2”. To get three equations perform any three operations to both the left hand side and right hand side of the equation one by one.

Complete step-by-step answer:
We have to construct three equations separately starting with $x=2$.
An equation is a mathematical sentence that has two equal sides separated by an equality sign. The two signs of the equality sign are called LHS (left hand side) and RHS (right hand side).
$''x=2''$ is also an equation.
We have to form three different equations, so we need to perform three different operations.
Let us 1st equation by adding ‘3’ to both sides of equation $''x=2''$.
On adding 3 to both sides of equation $''x=2''$, we will get,
$\begin{align}
  & x+3=2+3 \\
 & \Rightarrow x+3=5 \\
\end{align}$
This is our first equation which is obtained starting with $''x=2''$.
Now, let us construct the 2nd equation by subtracting ‘2’ to both sides of equation $''x=2''$.
On subtracting ‘2’ from both sides of the equation $''x=2''$ we will get,
$\begin{align}
  & x-2=2-2 \\
 & \Rightarrow x-2=0 \\
\end{align}$
This is our 2nd equation which is obtained starting from $''x=2''$.
Now, let us construct the 3rd equation by multiplying both sides of the equation with 5.
On multiplying both sides of equation $''x=2''$ with 5, we will get,
$\begin{align}
  & 5\times x=5\times 2 \\
 & \Rightarrow 5x=10 \\
\end{align}$
This is our 3rd equation which is obtained starting with $''x=2''$.
Hence, three equations that can be constructed starting from $''x=2''$:
$\begin{align}
  & x+3=5\ and \\
 & x-2=0\ and \\
 & 5x=10 \\
\end{align}$

Note: We can construct infinite such equations starting from $''x=2''$. Be careful that we can perform any operation but we need to perform the same operation to both sides of the equation so that values of the two sides of the equation remain the same. We can also use multiple operations for constructing equations like “ multiply by 4 then add 2 to both sides of the equation”.