Question

How do you solve \[4\left( {x - 5} \right) = 44\]using the distributive property?

Answer 1

Hint: In order to solve this question we must know the distributive property which is as follows:\[a(b + c) = ab + ac\],here a is distributed and multiplied with each of the numbers separated by operator and removes the bracket. By following the BODMAS, solve the further question in order to simplify. In our given question variable x and the number are not the like terms to be operated altogether so here we need to apply the Distributive property. We do not have to alter the equation inside the brackets just distribute the outer number with each of the inner numbers.

Complete step-by-step solution:
By applying the distributive property as per the question and substituting , we get
If we simplify further,
$\Rightarrow 4x - 20 = 44$
Adding both sides with 20 the LHS will have only 4x.
$\Rightarrow 4x = 44 + 20$
Calculating the sum , we have
$\Rightarrow 4x = 64$
Again to simplify further and get the value of x divide both sides by 4 in order to make the coefficient of x equal to 1 , we get the value of x
$\Rightarrow x = 16$
By solving with distributive property we got our value of x equal to 16.

Hence the correct answer is 16

Note: Distributive property is also known as the distributive law of multiplication and division.
We use the distributive property generally when the two terms inside the parentheses cannot be added or operated because they are not the like terms. We always have to ensure that the outside number is applied to all the terms inside the parentheses. Always solve the parentheses first as per the golden rule of BODMAS.