Question

Solve the following linear equation:
\[6(3m - 1) + 3(2m + 3) = 1 - 7m\]

Answer 1

Hint: To solve the given equation we will first multiply the terms with the terms in the bracket. Then we will simplify the equation obtained on multiplication. Since, the given equation has only one variable i.e., \[m\]. We will find the value of the variable by taking constant terms to one side of the equation and by further simplification.

Complete step-by-step answer:
Given, \[6(3m - 1) + 3(2m + 3) = 1 - 7m\]
On multiplying the terms with the terms in the bracket, we get
\[ \Rightarrow 18m - 6 + 6m + 9 = 1 - 7m\]
On adding \[7m\] on both the sides of the equation, we get
\[ \Rightarrow 18m - 6 + 6m + 9 + 7m = 1\]
Now, adding \[6\] on both the sides of the equation, we get
\[ \Rightarrow 18m + 6m + 9 + 7m = 1 + 6\]
On subtracting \[9\] from both the sides of the equation, we get
\[ \Rightarrow 18m + 6m + 7m = 1 + 6 - 9\]
On simplification, we get
\[ \Rightarrow 31m = - 2\]
On dividing both the sides by \[31\], we get
\[ \Rightarrow m = \dfrac{{ - 2}}{{31}}\]
Therefore, \[m = \dfrac{{ - 2}}{{31}}\].
So, the correct answer is “\[m = \dfrac{{ - 2}}{{31}}\]”.

Note: When we have a variable of a maximum of one order, then it is known as a linear equation in one variable. The general form of linear equation is \[jx + k = 0\], where \[j\] and \[k\] are two integers that can never be zero and the solution of \[x\] can be only one.
There are three types of linear equations:
\[(1)\] linear equation in one variable
\[(2)\] linear equation in two variables
\[(3)\] linear equation in three variables
Here, we have only one variable i.e., \[m\]. In these types of questions if there are \[n\] variables in an equation then there should be a minimum of \[n\] different equations, to get the value of all the variables. By substituting the values of variables in different equations we can get the values of different variables.