Question

How do you know when to use the distributive property when solving equations?

Answer 1

Hint: We can know when to use the distributive property when solving equations if we see more than 1 term in the parenthesis then we are going to use the distributive property. For example, if we have the equation $3\left( x+4 \right)=2$ then as you can see that two terms are written in parenthesis so we are multiplying 3 with the two terms one by one. And then we will combine the like terms together and hence, will solve.

Complete step by step solution:
There are the steps to use the distributive property which are as follows:
First of all, there should be a parenthesis which contains more than one term.
In the below, we are showing the following examples of what we said above:
$\begin{align}
  & 3\left( x+4 \right)=2; \\
 & 4\left( x-1+2 \right)=8 \\
\end{align}$
As you can see in the above two equations, more than one term is written inside the parenthesis. In the first equation, you can see two terms and in the second equation, you can see three terms.
Now, in the second step, we are going to distribute the terms written inside the parenthesis by multiplying the number written outside the parentheses one by one with all the terms written inside.
We are demonstrating one of the above equations.
$\begin{align}
  & 3\left( x+4 \right)=2 \\
 & \Rightarrow 3x+3\left( 4 \right)=2 \\
\end{align}$
As you can see that we have multiplied 3 by x and then we have multiplied 3 by 4 in the above equation.
In the third step, we are going to combine the like terms together. Now, simplifying the above equation we get,
$\Rightarrow 3x+12=2$
Subtracting 12 on both the sides we get,
$\Rightarrow 3x=2-12$
As you can see, we have written the terms (terms with no x variable on one side of the equation and terms with x variable on the other side of the equation).
The fourth step is the simplification using basic algebra so simplifying the above equation we get,
$\Rightarrow 3x=-10$
Dividing 3 on both the sides of the above equation we get,
$\Rightarrow x=-\dfrac{10}{3}$
This is how we are going to use the distributive property.

Note: To correctly use the distributive property, carefully all the steps which have described and illustrated in the above solution. The more examples involving distributive property are as follows:
$\begin{align}
  & 3x-4\left( 2x+5 \right)+4=20; \\
 & 2\left( 3x-1 \right)+5\left( 2x+8 \right)+1=19 \\
\end{align}$
Here you can see parentheses in the above two examples and more than one term inside the parenthesis so distributive property is applicable.