Question

How will you solve $9m + 2 = 3m - 10$ ?

$$A = - 5 \\\ B = 2 \\\ C = - 2 \\\ D = - 6 \\\$$

Answer 1

The key to solve this problem easily is to isolate $m$ term on one side and constant on the other side as we need to find the value of $m$ in the given equation. The given system of equations can be solved using elimination method and this deals with linear equations with one unknown.

Formula used: Addition or subtraction is used to isolate variable terms on one side of the equation while to solve the variable multiplication or subtraction is used.

Complete step by step solution:
Firstly from each side of the equation we will subtract $3m$ and $2$ .While keeping the equations balanced it will help in isolating the $m$ term on one side of the equation and constants on the other side of the equation.

$$\Rightarrow 9m + 2 - 3m - 2 = 3m - 10 - 3m - 2 \\\ \Rightarrow 9m - 3m + 2 - 2 = 3m - 3m - 10 - 2 \\\ \Rightarrow 9m - 3m + 0 = 0 - 10 - 2 \\\ \Rightarrow 9m - 3m = - 10 - 2 \\\$$

Now, simplify by combining like terms on each side of equation

$$\Rightarrow (9 - 3)m = - 12 \\\ \Rightarrow 6m = - 12 \\\$$

While keeping the equation balanced next we will divide each side of the equation by $6$ to solve for $m$ $\dfrac{{6m}}{6} = - \dfrac{{12}}{6}$
Later on simplify the equation by cancelling the term that are both in numerator and denominator and dividing the numbers
$m = - 2$
So the value of $m$ comes out to be $- 2$ which means option the correct option is $C$

Additional Information: To solve this problem in a better way it is important to simplify each side of the equation by removing parentheses and combining like terms. Addition or subtraction is used to isolate variable terms on one side of the equation while to solve the variable multiplication or subtraction is used.

Note: Remember that the solution of the linear equation is not affected if the same number is added or subtracted from both sides of the equation and if both the sides of the equation is multiplied or divided by the same non-zero number and a non-zero constant is never equal to zero.