Question

How do you solve $ 6\left( {3a + 1} \right) - 30 = 3\left( {2a - 4} \right) $ ?

Answer 1

Hint: The given question can easily be solved 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., $ x\left( {y + z} \right) = xy + xz $ . Here, in order to solve this question, we will have to use the same property and get the value of $ a $

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.
iv) Arrange terms so that variables and constants are opposite to the equal to sign.
v) Solve the equation and simplify, to get the desired unknown values.

Now, according to the question
Given is $ 6\left( {3a + 1} \right) - 30 = 3\left( {2a - 4} \right) $
We have to find the value of $ a $ 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( {3a} \right) + 6\left( 1 \right) - 30 = 3\left( {2a} \right) - 3\left( 4 \right) \\
   \Rightarrow 18a + 6 - 30 = 6a - 12 \\
  $
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 18a - 6a = - 12 - 6 + 30 \\
   \Rightarrow 12a = 12 \\
  $
Now, simplify the obtained equation by dividing it by $ 12 $ .
 $
   \Rightarrow \dfrac{{12a}}{{12}} = \dfrac{{12}}{{12}} \\
   \Rightarrow a = 1 \\
  $
Therefore, the value of $ a $ is $ 1 $ .

Note: The distributive property is one of the most frequently used properties in mathematics. Students can also double check their answer by substituting the value of $ a $ in the given equation.
 $
   \Rightarrow 6\left( {3a + 1} \right) - 30 = 3\left( {2a - 4} \right) \\
   \Rightarrow 6\left( {3\left( 1 \right) + 1} \right) - 30 = 3\left( {2\left( 1 \right) - 4} \right) \\
   \Rightarrow 6\left( {3 + 1} \right) - 30 = 3\left( {2 - 4} \right) \\
   \Rightarrow 6\left( 4 \right) - 30 = 3\left( { - 2} \right) \\
   \Rightarrow 24 - 30 = - 6 \\
  $
 $ \Rightarrow - 6 = - 6 $
Since L.H.S. = R.H.S. so, our answer is correct.