Question

How do you solve \[243=27r\] ?

Answer 1

Hint: In order to find a solution to this question, we will solve it as a one-step equation and substitute the solution for the variable in the equation and we will see if both sides of the equation are equal or not to know that our solution is correct.

Complete step by step answer:
As we can see our problem equation is a one-step equation. Therefore, we will solve it as a one-step equation.
A one-step equation is an equation that requires only one step to arrive at its solution.
Now, coming to our problem equation, we have:
\[\Rightarrow 243=27r\]
Now since it is a one-step equation, we will rewrite our equation so $r$ is on the left-hand side for our convenience.
Now by rewriting our equation, we get:
\[\Rightarrow 27r=243\]
Now, to isolate $r$ , we will divide both sides by $27$.
Therefore, on dividing both sides, we get our equation as:
\[\Rightarrow \dfrac{27r}{27}=\dfrac{243}{27}\]
On simplifying our equation, we get:
\[\Rightarrow r=9\]
Therefore, \[r=9\] is the final solution.
Now, we will check if our solution is correct or not.
Therefore, substituting \[r=9\] in the original equation and see if both sides of the equation are equal.
Therefore, on substituting, we get:
\[\Rightarrow 243=27\left( 9 \right)\]
On taking only right-hand side and equating, we get:
\[=243\]
Which is equal to the left-hand side.
\[\Rightarrow 243=243\]

Therefore, this concludes that our solution \[r=9\] is correct.

Note: While solving the problem of a one-step equation, after finding out our solution we have to check if both the sides are equal or not by substituting the solution for the variable in the equation.
For example:
\[\Rightarrow x+9=12\]
Subtract $9$ from both sides, we get:
\[\Rightarrow x=12-9\]
On simplifying, we get:
\[\Rightarrow x=3\]
Now check by substituting $3$ for \[x\] into the equation and solving, we get:
\[\Rightarrow 3+9=12\]
On simplifying, we get:
\[\Rightarrow 12=12~\], Hence checked our solution is correct.