Question

Solve the following equation.
 $ 7 - 5x = 5 - 7x $

Answer 1

Hint: We can find the value of x by either adding, subtraction or dividing similar value from both sides of the equation or by simply simplifying the equation and then finding the value accordingly.

Complete step-by-step answer:
Given. $ 7 - 5x = 5 - 7x $
To find. The value of x
We can solve the above to find the value of x by subtracting or adding similar terms on the side of the equation and simplifying it and finding the value accordingly.
Now, $ 7 - 5x = 5 - 7x $
Subtracting 7 from both side of the equation
 $ \Rightarrow 7 - 5x - 7 = 5 - 7x - 7 $
 $ \Rightarrow - 5x = - 7x - 2 $
Now, adding 7x on both side of the equation
 $ \Rightarrow - 5x + 7x = - 7x - 2 + 7x $
 $ \Rightarrow 2x = - 2 $
Dividing by 2 on both side of the equation
 $ \dfrac{{2x}}{2} = \dfrac{{ - 2}}{2} $
 $ \Rightarrow x = - 1 $
Hence, the value of x for $ 7 - 5x = 5 - 7x $ is -1.
To confirm the value we can cross check by putting the value $ x = - 1 $ in the given equation
 $ \Rightarrow 7 - 5x = 5 - 7x $
 $ \Rightarrow 7 - 5( - 1) = 5 - 7( - 1) $
 $ \Rightarrow 7 + 5 = 5 + 7 $
 $ \Rightarrow 12 = 12 $
Since, the left hand side of the equation is equal to the right hand side of the equation the value x equal to -1 is correct.
So, the correct answer is “-1”.

Additional Information.
We can solve alternatively also by directly simplifying the equation
 $ 7 - 5x = 5 - 7x $
 $ 7 - 5 = - 7x + 5x $
 $ 2 = - 2x $
 $ x = - 1 $
Hence, we can see that in both ways we can solve the equation, eventually we will land to the same answer.
Note: Both the methods are simple but the only thing we need to keep in mind is proper calculation. And also when the values are moved from the left hand side of the equation to the right hand side of the equation or vice versa the negative value will change to positive value or vice versa.