Question

How do you solve $ - 6\left( {3n - 3} \right) = - 90 $ using the distributive property?

Answer 1

Hint: The given question deals with the concept of distributive property. Distributive property refers to the multiplication of a number with the sum or difference of two numbers i.e., it is true for multiplication over addition and subtraction i.e., $ a\left( {b + c} \right) = ab + ac $ . Here, in order to solve this question, we will have to use the same property and get the value of $ n $ .

Complete step-by-step solution:
Distributive property helps in finding out the values of unknown variables if we follow four steps:
i) Multiplying the outer terms with the inner terms of parentheses.
ii) Then combining the like terms.
iii) Arrange terms so that variables and constants are opposite to the equal to sign.
iv) Let us solve the equation and simplify, to get the desired unknown values.

Now, according to the question
Given is $ - 6\left( {3n - 3} \right) = - 90 $
We have to find the value of $ n $ by using distributive property in the given equation.
Following step one of solving distributive property related questions i.e., to multiply the outer terms with inner terms of parentheses, we get,
 $
   \Rightarrow - 6\left( {3n} \right) - 6\left( { - 3} \right) = - 90 \\
   \Rightarrow - 18n + 18 = - 90 \\
  $
Next, we combine the like terms and arrange them in such a way that variables and constants are opposite to the equal to sign and we get,
 $ \Rightarrow - 18n = - 90 - 18 $
Now, simplify the obtained equation
 $
   \Rightarrow - 18n = - 108 \\
   \Rightarrow n = \dfrac{{ - 108}}{{ - 18}} \\
   \Rightarrow n = 6 \\
  $
Therefore, the value of $ n $ is $ 6 $ .

Note: The distributive property is one of the most frequently used property in mathematics. Students can also double check their answer by substituting the value of $ n $ in the given equation.
 $
   \Rightarrow - 6\left( {3n - 3} \right) = - 90 \\
   \Rightarrow - 6\left( {3\left( 6 \right) - 3} \right) = - 90 \\
   \Rightarrow - 6\left( {18 - 3} \right) = - 90 \\
   \Rightarrow - 6\left( {15} \right) = - 90 \\
   \Rightarrow - 90 = - 90 \\
  $
Since L.H.S. = R.H.S. so, our answer is correct.