Question

How do you solve \[3\left( 2x+7 \right)=27\] using distributive property?

Answer 1

Hint: We will solve this question using distributive property. First we have to multiply the LHS using a distributive formula. After that we have to simplify the equation by grouping like terms. After that we have to simplify it further to get the value of x.

Complete step by step solution:
Let us know about distributive property.
The definition of the distributive property is that multiplying a number by a sum is the same as doing each multiplication separately.
In equation form, it will look like
\[a\left( b+c \right)=ab+ac\]
Using this formula we will solve this question.
Given equation is
\[3\left( 2x+7 \right)=27\]
We can see that our LHS is in the form of \[a\left( b+c \right)\]. So we can apply distributive property.
Now we have to apply distributive property for our LHS.
We will get
\[\Rightarrow 6x+21=27\]
Now we have to group like terms.
So we will keep x containing terms on LHS and remaining on RHS side.
Now we will subtract 21 from both sides of the equation.
\[\Rightarrow 6x+21-21=27-21\]
By simplifying we will get
\[\Rightarrow 6x=6\]
Now to simplify it further we will divide with 6 on both sides of the equation.
\[\Rightarrow \dfrac{6x}{6}=\dfrac{6}{6}\]
By simplifying further we will get
\[\Rightarrow x=1\]
By solving the given equation we will get \[x=1\].

Note: We can also do it without using distributive property. First by dividing the equation with 3 and then by simplifying the equation we will get the result. We can also check the solution by substituting this value in the equation and check whether it is satisfied or not.