Question

How do solve \[12\left( {x + 20} \right) = 372\]using the distributive property?

Answer 1

Hint: We have to solve the expression by the distributive property. The distributive property is also known as the distributive law of multiplication. To solve the given expression first of all we have to know about distributive property which means to distribute something or to divide something. The three properties mostly used for numbers are distributive property, associative property and commutative property. The definition of the distributive property is the multiplication of a number with the sum or difference of two numbers, which implies the distributive property. The equation becomes easier to solve when we use the distributive property of multiplication. In the given equation, we will multiply twelve inside the parenthesis and then we will subtract two hundred forty from both sides of the equation.

Complete step by step answer:
Step : 1 the given expression is $12\left( {x + 20} \right) = 372$,
$ \Rightarrow a\left( {b + c} \right) = ab + ac$
Step: 2 Use the distributive property to expand the expression.
$12 \times x + 12 \times 20 = 372$
Now simplify the equation to write it into its simplest form.
$ \Rightarrow 12x + 240 = 372$
Step: 3 subtract 240 to both sides of the equation to simplify it.
$
   \Rightarrow 12x + 240 - 240 = 372 - 240 \\
   \Rightarrow 12x = 132 \\
 $
Step: 4 divide both sides of the given equation by 12 , to find the value of $x$ .
$ \Rightarrow 12x = 132$
$ \Rightarrow \dfrac{{12x}}{{12}} = \dfrac{{132}}{{12}}$
Simplify the equation to find the result.
$ \Rightarrow x = 11$

Note: students are advised to use the distributive property of multiplication to solve the given expression. The distributive property is defined as, $a\left( {b + c} \right) = ab + ac$, the multiplication of numbers in a specific manner. They should not make mistakes, while solving the equation. Students can also solve the given equation by doing simple multiplication.