Question

Solve the following equation: $n + 5 = 19(n - 1)$

Answer 1

Hint: To solve this type of linear equation we will take variable terms to one side and constants to the other side then we will apply different mathematical operations to get the required solution.

Complete answer:
Given that the equation $n + 5 = 19(n - 1)$ and then we need to find the value of the unknown variable $n$ , we will make use of the basic mathematical operations to simplify further.
Using the multiplication operation, we get $n + 5 = 19(n - 1) \Rightarrow n + 5 = 19n - 19$
now Turing the variables on the left-hand side and also the numbers on the right-hand side we get $n + 5 = 19n - 19 \Rightarrow n - 19n = - 19 - 5$ while changing the values on the equals to, the sign of the values or the numbers will change.
Now by the subtraction operation, we get $ - 18n = - 24$ for example; $3x - 5x = x(3 - 5) = - 2x$ which is also applicable for the subtraction of the variables.
Hence making use of the division operation we have $n = \dfrac{{ - 24}}{{ - 18}}$, the two signs are negative and hence they cancel each other, also divide them with the multiple two, we get $n = \dfrac{{ - 24}}{{ - 18}} \Rightarrow n = \dfrac{{12}}{9}$
Now divide them with the multiple three we have $n = \dfrac{4}{3}$ or in the decimal form $n = 1.333$ which is the required unknown variable

Note:
There are three methods to solve linear equations in one variable.
1. Trial and Error.
2. Inverse operations.
3. Transposition Method.