Question

How do you solve $2x+9=2x-9$?

Answer 1

Hint: Try to get the value of ‘x’ for the given equation. First subtract 9 from both the sides. Then subtract $2x$ from both the sides. If the final equation does not contain any variable, then the given equation has no solution or we can say that the solution is the null set.

Complete step by step answer:
Solving this question means we have to find the value of ‘x’ for which the equation gets satisfied.
Considering the equation $2x+9=2x-9$
Subtracting ‘9’ from both the sides of the equation, we get
$\begin{align}
  & 2x+9-9=2x-9-9 \\
 & \Rightarrow 2x=2x-18 \\
\end{align}$
Subtracting $2x$ from both the sides, we get
$\begin{align}
  & \Rightarrow 2x-2x=2x-2x-18 \\
 & \Rightarrow 0=0-18 \\
 & \Rightarrow 0=-18 \\
\end{align}$
$\Rightarrow 0=18$ (By multiplying $-1$ both the sides )
Since it does not contain any variable ‘x’ hence there is no solution for the given equation.
And because 0 does not equal to 18, the solution to this question is the null set i.e. $x=\phi $

Note: For solving an equation, the equation should contain the variable at last. If the equation is free from the variable or contains the same variable with the same coefficient on both sides of the equation, then there is no solution for the given equation or we can say that the solution to the given equation is the null set. As we know 0 can not be equal to 18, so the solution we are getting $0=18$ has no meaning and hence it has no solution or It’s solution is the null set.