Question

How do you solve \[7\left( x+2 \right)+3=73\] using the distributive property?

Answer 1

Hint: This is one of the very common problems in linear algebra and these types of problems are pretty straight forward and are very easy to solve. These are simple linear equations which can be solved by analytical method as well as graphical method. First we need to understand what distributive property is. The distributive property for a set of integers, say, \[a\] , \[b\] , \[c\] is defined as,
\[a\left( b+c \right)=a\cdot b+a\cdot c\] . Now using the above property, we can very easily solve the above given problem.

Complete step by step answer:
Now starting off with the solution and applying the property as discussed above, we write,
\[\begin{align}
  & 7\left( x+2 \right)+3=73 \\
 & \Rightarrow 7\cdot x+7\cdot 2+3=73 \\
\end{align}\]
Now, multiplying each and every pair on the left hand side of the equation we get,
\[7x+14+3=73\]
We now add the like terms of the equation on the left hand side and get,
\[7x+17=73\]
Rearranging the terms on the right hand side of the equation we get,
\[\begin{align}
  & 7x=73-17 \\
 & \Rightarrow 7x=56 \\
\end{align}\]
Now, from this step, we can very easily find the value of \[x\] by simply dividing the right hand side of the equation with the coefficient of \[x\] . In our case the coefficient of \[x\] is \[7\] . On dividing we get,
\[\begin{align}
  & x=\dfrac{56}{7} \\
 & \Rightarrow x=8 \\
\end{align}\]
Thus, we get the value of \[x\] from the above problem as \[8\] . We can also verify whether our answer is correct or not by putting the value \[x=8\] in our original given problem and check if the left hand side is equal to the right hand side or not.

Note:
First of all, we must not confuse the distributive property with the associative property, as most of the students commit a mistake here. We can also solve the problem by keeping the $\left( x+2 \right)$ term intact and perform addition, subtraction and other operations on the rest part. Finally, we get a equation in terms of $\left( x+2 \right)$ and then we subtract $2$ from both sides of the equation to get the value of $x$ .