Question

How do you solve \[ - 8m + 12 = - 2m + 27\]?

Answer 1

Hint: This is a linear equation in only one variable. Take constants on one side and the term having variables on the other side. Then divide both sides of the equation with a suitable number to find the value of the variable.

Complete step by step answer:
According to the question, a linear equation in one variable is given to us and we have to show how to solve it.
The given equation is:
\[ - 8m + 12 = - 2m + 27\]
For solving this, first we’ll transfer 12 from left hand side to right hand side of the equation and $ - 2m$ from right hand side to left hand side of the equation, we’ll get:
\[ - 8m + 2m = - 12 + 27\]
Simplifying this equation further, we’ll get:
\[ - 6m = 15\]
Dividing both sides of the equation by -6, well get:
\[ \dfrac{{ - 6m}}{{ - 6}} = \dfrac{{15}}{{ - 6}}\]
In the left hand side, -6 will get cancelled out from the numerator and denominator. And in the right hand side, we can solve it as:
\[
    m = \dfrac{{3 \times 5}}{{ - 3 \times 2}} \\
   \Rightarrow m = - \dfrac{5}{2}
 \]

Thus, the value of variable $m$ in the equation is \[ - \dfrac{5}{2}\].

Additional Information:
An equation in one variable with the highest power of variable in the equation as 1 is called a linear equation in one variable. If the highest power is 2 then it is called a quadratic equation and if the highest power is 3 then it is called a cubic equation. To generalize it, if the highest power is n then it is called the nth degree equation.
This condition is valid if all the powers of the variable throughout the equation are non negative integers.

Note: If a linear equation is having only one variable, it can be solved directly to get the value of the variable. If it was a two variable equation, we couldn’t have solved it. To determine the values of two different variables, we need a system of two different equations in those variables and to determine three variables we need a system of three equations in those variables. Similarly if there are $n$ different variables then we require $n$ different equations to find their values.