Question

Solve \[7 + 2\left( {a + 1} \right) - 3a = 5a\]

Answer 1

Hint: Here we are asked to solve the given equation to find the value of the unknown variable. A simple equation with only one unknown variable can be solved by a method called the transposition method. In this method, the terms having unknown variables are collected at one side of the equation and the other terms at the other side. Then by simplifying the equation we will get the value of the unknown variable.

Complete step by step answer:
It is given that \[7 + 2\left( {a + 1} \right) - 3a = 5a\], we aim to solve this equation to find the value of the unknown variable. Here the unknown variable is \[a\].
We will be solving this equation by the transposition method. According to that method first, the terms having unknown variables are collected at one side of the equation.
Consider the given equation \[7 + 2\left( {a + 1} \right) - 3a = 5a\], let us simplify the second term on the left-hand side of the equation.
\[ \Rightarrow 7 + 2a + 2 - 3a = 5a\]
Now let us keep all the terms containing the unknown variable on the left-hand side of the equation by transferring the other terms to the right-hand side.
\[ \Rightarrow 2a - 3a - 5a = - 7 - 2\]
Now let us simplify the terms on both sides.
\[ \Rightarrow - 6a = - 9\]
Now let us transfer the term \[ - 6\] on the left-hand side to the right-hand side.
\[ \Rightarrow a = \dfrac{{ - 9}}{{ - 6}}\]
On simplifying the above equation, we get
\[ \Rightarrow a = \dfrac{3}{2}\]
Thus, we have found the value of the unknown variable \[a\] as \[\dfrac{3}{2}\].

Note:We also have two other methods to solve a simple equation with only one unknown variable; they are the trial-and-error method and the systematic method. We have used the transposition method to solve this problem since it takes less time to solve a problem than the other two methods. We can also check whether our answer is correct or not by substituting the value in the given equation.