Question

Find the value of m from the given equation $m + 4\left( {2m - 3} \right) = - 3$ ?

Answer 1

Hint: In this question, we are given a linear equation in one variable and we have been asked to not only find the solution, but also to write the steps. So, first simply open the brackets by multiplying the constant with the terms inside the bracket. Then, shift the terms and find the value of $m$.

Complete step-by-step solution:
We are given an equation $m + 4\left( {2m - 3} \right) = - 3$ and we have been asked to find the value of $m$.
$ \Rightarrow m + 4\left( {2m - 3} \right) = - 3$
Step 1: Multiply the constant outside bracket with the terms inside brackets using distributive property.
$ \Rightarrow m + \left( {4 \times 2m} \right) - \left( {4 \times 3} \right) = - 3$
Step 2: Now, simplify the equation.
$ \Rightarrow m + 8m - 12 = - 3$
Step 3: Bring the like terms together and add them.
$ \Rightarrow 9m = 9$
Step 4: Shift to find the required value of $m$.
$ \Rightarrow m = \dfrac{9}{9} = 1$
Hence, $m = 1$.

Therefore the value of m is equal to 1.

Note: The equation given to us is a linear equation in one variable. There are many types of equations. But what is an equation?
An equation is simply an expression which has a sign of “equals”. But these equations are not simple. They can either be linear, quadratic, cubic, etc. This depends upon the degree of the equation. An equation with highest degree 1 is called a linear equation. The equation given in the question is a linear equation. An equation with highest degree 2 is called a quadratic equation, and that with the highest degree 3 is called a cubic equation.
Furthermore, these equations can be in one, two, three or many variables. Let us see certain examples.
1) $4x = 8$- this equation is a linear equation in one variable.
2) $3x + 6y = 18$ - this equation is a linear equation in two variables.