Question

How do you solve $5 = r - 1 - 3r$?

Answer 1

Hint: We are given the linear equation with variable $r$. To solve this equation, our first step is to combine the like terms with variable $r$. After that, we will remove the additional terms connected with the variable by performing opposite operations to get our final answer.

Complete step by step solution:
We are given $5 = r - 1 - 3r$.
Our first step is to combine the like terms with variable $r$. Form the equation we can easily identify that $r$ and $ - 3r$ are the like terms on the right hand side of the equation, Therefore we can rewrite the equation as:
$ \Rightarrow 5 = r - 3r - 1$
Now, combining both the like terms, we get
$ \Rightarrow 5 = - 2r - 1$
Now, we can see that there is an additional term on the right hand side of the variable where the variable is present which is 1 and is subtracted from the term containing the variable. Therefore, to remove this, we will add 1 to both the sides of the equation.
$
   \Rightarrow 5 + 1 = - 2r - 1 + 1 \\
   \Rightarrow 6 = - 2r \\
$
We can observe that $ - 2$ is multiplied with the variable $r$. To remove it, we have to divide both sides of the equation by $ - 2$.
$
   \Rightarrow \dfrac{6}{{ - 2}} = \dfrac{{ - 2r}}{{ - 2}} \\
   \Rightarrow - 3 = r \\
   \Rightarrow r = - 3 \\
$

Thus, by solving this equation we get $r = - 3$ as our final answer.

Note: While solving any linear equation, we need to keep in mind that whatever operation we perform, we have to perform it on both the sides of the equation. This is because the equation must be in balanced condition. If we perform any operation on only one side, it will become unbalanced and as a result, we will get the incorrect answer.