Question

How do you solve $ 8(1 + 7n) = 8( - 2 + 6n)? $

Answer 1

Hint: If any equation involves only one variable and the highest order of the variable is one, then that equation is said to be a linear equation. Here we will simplify the equation by using the basic mathematical operations and will find the value of the unknown term or the variable “n”.

Complete step-by-step solution:
Take the given equation –
 $ \Rightarrow 8(1 + 7n) = 8( - 2 + 6n) $
Open the brackets multiplying the constant terms if any as such on the right hand side of the equation. Also, remember when there is a positive term outside the bracket then the sign of the terms inside the bracket remains the same.
 $ \Rightarrow 8 + 56n = - 16 + 48n $
Bring all the variables at one side and the constants on the other side of the equation – Also; remember that the sign of the term is changed when moved from one to another. Positive changes to negative and negative changes to positive.
 $ \Rightarrow 56n - 48n = - 16 - 8 $
Simplify the above equation –
 $ \Rightarrow 8n = - 24 $
When the term in the multiplicative at one side, moved to another side of the equation, then it goes to the denominator-
 $ \Rightarrow n = - \dfrac{{24}}{8} $
Find the factors for the term on the numerator on the right –
 $ \Rightarrow n = - \dfrac{{8 \times 3}}{8} $
Common multiples from the numerator and the denominator cancel each other, therefore remove from the numerator and the denominator.
 $ \Rightarrow n = ( - 3) $ is the required answer.

Thus the final answer is n=-3.

Note: Remember the difference between the two most commonly used concepts in mathematics, the variables and the constant. Variable is the value which has the ability to change whereas, the constants are the terms which remain unchanged and have the fixed value.