Question

How do you solve $ 42 = - 6( - 3n + 6) + 6(n - 3) $ using the distributive property?

Answer 1

Hint: Here we will first take the given expression and apply the distributive property opening the brackets also be careful about the negative sign outside the bracket and then simplify for the resultant value for “n”.

Complete step by step solution:
Distributive property which says that the sum of two or more addends/ terms multiplied by a number gives the same answer as distributing the multiplier, multiplying each addend separately and adding the products together.
Take the given expression: $ 42 = - 6( - 3n + 6) + 6(n - 3) $
Apply Distributive property in the given above expression, while opening the bracket be careful about the sign convention. When there is a negative sign outside the bracket the sign of the terms inside the bracket changes whereas if there is a positive term outside the bracket then there is no change in the sign of the terms inside the bracket.
 $ 42 = 18n - 36 + 6n - 18 $
Simplify the above equation finding the pair of like terms on the right hand side of the equation.
 $ 42 = \underline {18n + 6n} - \underline {36 - 18} $
Simplify among the like terms, when you simplify between the two negative terms, do addition and give negative sign to the resultant value.
 $ 42 = 24n - 54 $
Move term with constant on the left hand side of the equation. When you move any term from one side to another, the sign of the term also changes. Negative terms become positive and vice-versa.
 $ 42 + 54 = 24n $
Simplify the above equation.
 $ 96 = 24n $
The above equation can be re-written as: $ 24n = 96 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ n = \dfrac{{96}}{{24}} $
Find factors for the above expression,
 $ n = \dfrac{{24 \times 4}}{{24}} $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the above expression.
 $ x = 4 $
This is the required solution.
So, the correct answer is “ $ x = 4 $ ”.

Note: Be careful about the sign convention. When you find the product of one positive and other negative term the resultant value is in negative and when you find the product of two negative terms the resultant value is in positive.