Question

Solve the following equation: $ 2x + 6 = 7x - 8 $ .

Answer 1

Hint: The given equation is a one-step equation. If we perform any operation of addition, subtraction, multiplication and division with the same number on both sides of the equation, then the both sides of the equation will remain equal.

Complete step by step solution:
In this problem, we have given an equation $ 2x + 6 = 7x - 8 $ . Now, to solve the equation we need to add $ 8 $ on both sides of the equation and on adding we get,
 $ \Rightarrow 2x + 6 + 8 = 7x - 8 + 8 $
On further solving, we get,
 $ \Rightarrow 2x + 14 = 7x $
Now, we will subtract $ 14 $ from both the sides of the equation,
 $ \Rightarrow 2x + 14 - 14 = 7x - 14 $
On further solving, we get,
 $ \Rightarrow 2x = 7x - 14 $
Now, we will subtract $ 2x $ from both the sides,
 $ \Rightarrow 2x - 2x = 7x - 14 - 2x $
Only the like terms, whose variables are the same can be added or subtracted. Now, on further solving, we get,
 $ \Rightarrow 0 = 5x - 14 $
Now, we will add $ 14 $ on both sides of the equation,
 $ \Rightarrow 0 + 14 = 5x - 14 + 14 $
On further solving, we get,
 $ \Rightarrow 14 = 5x $
Now, we will divide the whole equation by $ 5 $ ,
 $ \Rightarrow \dfrac{{14}}{5} = \dfrac{5}{5}x $
On further solving, we get,
 $ \Rightarrow \dfrac{{14}}{5} = x $
Hence, the value of x is $ \dfrac{{14}}{5} $ .
So, the correct answer is “ $ \dfrac{{14}}{5} $ ”.

Note: We can also solve the given equation in the question by taking like terms on one side and then solving it, when the positive term goes from one side of the equation to the other then it becomes negative and vice versa and when the number is in the multiplication with the other and when it goes from one side to other then this will divide the other number and vice versa.