Question

How do you solve \[2\left( x-5+2 \right)=6\] using distributive property?

Answer 1

Hint: 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 methods. 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 this 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,
\[\begin{align}
  & 2\left( x-5+2 \right)=6 \\
 & \Rightarrow 2\cdot x+2\cdot \left( -5 \right)+2\cdot 2=6 \\
\end{align}\]
Now, taking out the negative sign out of the bracket from the second term of the equation \[2\cdot x+2\cdot \left( -5 \right)+2\cdot 2=6\] , we get,
\[2\cdot x-2\cdot 5+2\cdot 2=6\]
Now, multiplying each and every pair on the left hand side of the equation we get,
\[2x-10+4=6\]
We now add the like terms of the equation on the left hand side and get,
\[2x-6=6\]
Rearranging the terms on the right hand side of the equation we get,
\[2x=12\]
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 \[2\] . On dividing we get,
\[\begin{align}
  & x=\dfrac{12}{2} \\
 & \Rightarrow x=6 \\
\end{align}\]
Thus, we get the value of \[x\] from the above problem as \[6\] .

Note:
Regarding the above problem, we must remember the distributive law or else we won’t be able to solve the problem. The given sum can also be solved graphically. In such a case we assume the given linear equation as \[y\] and plot the straight line on the graph paper. The point of intersection of this line and the \[x\] -axis gives us the required answer.