How do you solve $ - 4 + 6x = - 3x - 31? $

Hint: Take the given expression and move constants on one side of the equation and all the terms with the variable on the opposite side and then simplify the equation for the resultant required value for “x”.

Complete step by step solution:
Take the given expression: $ - 4 + 6x = - 3x - 31 $
Move the term with the variable on the left hand side of the equation and all the constants on the opposite sides. When you move any term from one side to the another then the sign of the term also changes. Positive terms become negative and the negative term becomes positive.
 $ 6x + 3x = - 31 + 4 $
Simplify the above equation finding the addition of the terms on the both the sides of the equation. When you find addition for one negative and the other positive term then you have to do subtraction and give negative sign to the resultant value.
 $ 9x = - 27 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ x = - \dfrac{{27}}{9} $
Find the factors for the numerator in the above expression.
 $ x = - \dfrac{{3 \times 9}}{9} $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator from the above expression.
 $ x = - 3 $
This is the required solution.
So, the correct answer is “ $ x = - 3 $ ”.

Note: Be careful about the sign convention while simplification. While doing simplification remember a 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.