Question

How do you solve $12r-18=13r+18$?

Answer 1

Hint: Now to solve the given equation we will first bring all the variable terms on one side and all the constant terms on the other side. Now we will simplify the equation and divide the whole equation by the coefficient of r. hence we get the solution of the equation.

Complete step by step answer:
Now consider the given equation $12r-18=13r+18$
We know that this is a linear equation in one variable. We want to find the solution of the equation which means we want to find the value of r for which the equation holds true.
Now first let us subtract 12r on both sides of the equation. Hence we get,
$\begin{align}
  & \Rightarrow 12r-12r-18=13r-12r+18 \\
 & \Rightarrow -18=r+18 \\
\end{align}$
Now subtracting 18 on both sides of the equation we get,
$\begin{align}
  & \Rightarrow -18-18=r \\
 & \Rightarrow -36=r \\
\end{align}$
Hence we have the value of r must be – 36.

Hence the solution of the equation is r = - 36.

Note: Now always note that the solution obtained will satisfy the equation. Hence always remember to check the solution by re-substituting the solution in the equation. If the solution is true then it will satisfy the equation. If the solution is incorrect we will arrive at a contradiction. Also note that we can transpose terms from one side of the equation to the other side of the equation. While transposing the terms from one side to another remember that the sign of terms will change.