Question

Solve for \[m\]:\[\dfrac{{8 - m}}{3} = m\]

Answer 1

Hint:
Here, we will solve the equation by using basic mathematical operations. First, we will isolate the variable on one side, so for that, we will cross multiply the terms and then add the variable terms together. Then we will divide both sides of the equation by the coefficient of the variable to get the required answer.

Complete step by step solution:
We are given a linear equation \[\dfrac{{8 - m}}{3} = m\].
Now, we will multiply \[3\] to both the sides of the equation such that the denominator on the left side of the equation vanishes to one. So, we get
\[ \Rightarrow \dfrac{{8 - m}}{3} \times 3 = m \times 3\]
\[ \Rightarrow 8 - m = 3m\]
Adding \[m\] on both the sides, we get
\[ \Rightarrow 8 = 3m + m\]
Now, by simplifying the equation, we get
\[ \Rightarrow 4m = 8\]
Now, we will divide by \[4\] on both the sides of the equation. Therefore, we get
\[ \Rightarrow \dfrac{{4m}}{4} = \dfrac{8}{4}\]
\[ \Rightarrow m = 2\]

Therefore, the solution for \[m\] is \[2\].

Additional Information:
We can solve the linear equation by putting the variable on the left-hand side and the numerical values on the right-hand side. We will then change the operators’ sign while changing sides of the terms and thus we can solve for the variable. Similarly, we have linear equations in two variables, linear equations in three variables, and so on. We can solve the linear equations in two variables by using the method of elimination and method of substitution and the linear equations in three variables by using the matrix method.

Note:
We know that Linear equations are a combination of constants and variables. A linear equation is defined as an equation with the highest degree as 1. Constants are the numbers whereas variables are represented in letters. We should also know that every linear equation in one variable has a one and unique solution. Linear equations are formed with variables such that the variable is solved to find the value.