Question

How do you solve 2m + 12 = 3m – 31?

Answer 1

Hint: Here, in this problem we are going to solve a simple algebraic linear equation. Solving algebraic linear equations are much simpler and easier than solving quadratic or cubic equations. Usually solving some equation is nothing but finding the unknown variable’s value. Now we are going to do the same in this problem. In this problem, the given linear equation is 2m + 12 = 3m – 31. We are just going to simplify it in a simple manner to solve this equation and to get the value of m. We can do it in a step by step manner.

Complete step-by-step solution:
We know that the given linear equation is
2m + 12 = 3m – 31
Now we can balance the equation by subtracting 3m on both sides.
We will get the balanced equation after subtracting it with 3m, that is
2m + 12 – 3m = 3m – 31 – 3m
\[\begin{align}
  & \Rightarrow 12-m=-31 \\
 & \Rightarrow -m=-31-12 \\
 & \Rightarrow -m=-43 \\
\end{align}\]
Here we can multiply – 1 on both sides to get the value of m.
After multiplying with – 1, we get
 \[\begin{align}
  & \Rightarrow -\left( -m \right)=-\left( -43 \right) \\
 & \Rightarrow m=43 \\
\end{align}\]
Therefore, the value of m is 43.

Note: Even though it is a simple linear equation, students may make mistakes in the sign part, that is plus and minus symbols. In this question, 3m has been subtracted in the given equation in order to balance it, but we can use any of the same numbers from the equation with opposite symbols to simplify it.