Question

How do you solve $ - 4 = 5n + 6? $

Answer 1

Hint: First of all take all the given expression and frame the equation in such a way that all the constants on one side and the term with the variable on the opposite side then simplify the given expression for the resultant required value for “n”.

Complete step by step solution:
Take the given expression: $ - 4 = 5n + 6 $
The above equation can be re-written as: $ 5n + 6 = - 4 $
Move the constant from the left hand side of the equation to the right hand side of the equation. When you move any term from one side of the equation to the opposite side then the sign of the term also changes. Negative terms become positive and vice-versa.
 $ 5n = - 4 - 6 $
Now, when you simplify the two like terms both having the negative sign then you have to do addition and given sign of negative to the resultant value.
 $ 5n = - 10 $
Term multiplicative on one side if moved to the opposite side, then it goes to the denominator.
 $ n = - \dfrac{{10}}{5} $
Find factors for the numerator on the right hand side of the equation.
 $ n = - \dfrac{{5 \times 2}}{5} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the numerator and denominator in the above equation.
 $ n = - 2 $
This is the required solution.
So, the correct answer is “ $ n = - 2 $ ”.

Note: Be careful about the sign convention while moving any term from one side to another. While doing simplification remember the few rules. Addition of two positive terms gives the positive term, Addition of one negative and positive term, you have to do subtraction and give sign of bigger number whether positive or negative and addition of two negative numbers gives negative number but in actual you have to add both the numbers and give negative sign to the resultant answer.