Question

Solve the given equation in x: $ 4\left( x+1 \right)=4x+10 $ .

Answer 1

Hint:
We start solving the problem by performing the multiplication operation on the L.H.S (Left Hand Side) of the given equation in the problem. After completing the multiplication operation, we subtract both sides of the resultant equation with $ 4x $ which gives contradictory equality making the given equation not solvable and with no solution for the given equation.

Complete step by step answer:
According to the problem, we are asked to solve the given equation: $ 4\left( x+1 \right)=4x+10 $ .
Now, we have $ 4\left( x+1 \right)=4x+10 $ .
 $ \Rightarrow 4x+4=4x+10 $ ---(1).
Let us subtract $ 4x $ from both sides of the equation (1).
 $ \Rightarrow 4x+4-4x=4x+10-4x $ .
 $ \Rightarrow 4=10 $ ---(2).
From equation (2), we can see that we have found 4 = 10. Which is a contradiction as they both are not equal. So, there is no value for x satisfying the given equation of the problem: $ 4\left( x+1 \right)=4x+10 $ .
 $ \therefore $ The equation given in the problem: $ 4\left( x+1 \right)=4x+10 $ does not have a solution.

Note:
We can see that we have equal coefficients for x terms on both sides of the equations, which means that the constant on both sides have to be equal in order to attain equality of the given equation. We can also verify the result by making use of the trial and error method for the value of x which satisfies the given equation. Whenever we get this type of problem, we should try to find the values of x which absolutes give the result L.H.S (Left Hand Side) equal to R.H.S (Right Hand Side).