Question

How do you solve $ - 4(3x - 2) = - 32 $ using the distributive property?

Answer 1

Hint: Here we will take the given expression and apply the distributive property opening the brackets and then simplified for the resultant value for “x”. We must know that it is a linear equation in one variable.

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: $ - 4(3x - 2) = - 32 $
Apply Distributive property in the given above expression,
 $ - 4(3x) - ( - 4)(2) = - 32 $
Simplify the above equation finding the product of two terms. Product of one negative and one positive term gives resultant value in negative and product of two negative terms gives resultant value in positive.
 $ - 12x + 8 = - 32 $
Move term with variable on the right hand side of the equation and constant from the right hand side of the equation to 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.
 $ 8 + 32 = 12x $
The above equation can be re-written as: $ 12x = 40 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ x = \dfrac{{40}}{{12}} $
Find factors for the above expression,
 $ x = \dfrac{{20}}{{6}} $
Common factors from the numerator and the denominator cancel each other. Therefore, remove from the above expression.
 $ x = \dfrac{10}{3} $
This is the required solution.
So, the correct answer is “ $ x = \dfrac{10}{3} $ ”.

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