Question

How do you solve \[8\left( m-5 \right)=2\left( m-8 \right)\]?

Answer 1

Hint:
 The above question is a simple problem of linear equations in one variable. So, we will simply first understand the concept and definition of linear equation in one variable and then we will solve the above question to get the value of ‘m’. We will first open the parenthesis in the RHS and then shift all constant terms at the RHS and all the variable terms at the LHS. Then we will simplify the obtained equation by using the basic algebraic operations. Then we will get the value of m.

Complete step by step answer:
We know that the linear equation in one variable is an equation that has a maximum of one variable in the equation which is of order 1. Also, we know that a linear equation in one variable has only one solution.
And, also the standard form of linear equation in one variable is represented as:
ax + b = 0 where a, b is real number and a is not equal to zero.
So, we can say that \[8\left( m-5 \right)=2\left( m-8 \right)\] is a linear equation in one variable with variable m.
First, we will open the parenthesis at the RHS and the LHS, then we will get:
\[\begin{align}
  & \Rightarrow 8\left( m-5 \right)=2\left( m-8 \right) \\
 & \Rightarrow 8\times m-8\times 5=2\times m-2\times 8 \\
\end{align}\]
Now, performing the multiplication and simplifying further we get
\[\Rightarrow 8m-40=2m-16\]
Now, to solve \[8m-40=2m-16\] we will shift variable on one side of the equation from other side of the equation and similarly, we will shift constant on the same side of the equation.
\[\Rightarrow 8m-2m=-16+40\]
\[\Rightarrow 6m=24\]
So, after dividing both side by 6 we will get:
 $ \begin{align}
  & \Rightarrow \dfrac{6m}{6}=\dfrac{24}{6} \\
 & \Rightarrow m=4 \\
\end{align} $
Now, when we will put m = 6 in the equation, then we will get -8 = -8, which satisfies the equality.
Hence, m = 4 is our required answer.

Note:
Students is required to recall the linear equations and basic properties of linear equations to solve these types of questions. We can verify the answer by putting the value in the given equation. On solving the equation if we get the values of LHS and RHS equal it means that the answer is correct. Students are also required to note that when we shift variable or constant from one side of the equation to the other side of the equation then the sign of the variable get reversed and magnitude remains same.