Question

What will be the solution to \[9e - 7 = 7e - 11\] ?

Answer 1

Hint: Since we need to find the value of \[e\] so it must be placed on one side and numbers should be placed on the other side. : The key to find the solution is to always do the same thing on both sides of the equation while keeping the equation balanced. Later on fill the value of in equation \[e\] to recheck whether the solution is correct.

Complete step-by-step solution:
Firstly to find value of \[e\] simplify the equation by the help of basic algebra
\[
   \Rightarrow 9e - 7 = 7e - 11 \\
   \Rightarrow 9e - 7e = - 11 + 7 \\
   \Rightarrow 2e = - 4 \\
 \]
Now further dividing both the sides by \[2\] and cancelling the term that is both in numerator and denominator we get
\[
   \Rightarrow \dfrac{{2e}}{2} = \dfrac{{ - 4}}{2} \\
   \Rightarrow e = - 2 \\
 \]

Additional information: We can also solve this equation by making everything to zero. It is important to remember that to remove the number it is important to decide how to remove it and we need to do the opposite of what is currently done.

Notes: We can verify whether the solution is correct by substituting the value of \[e\] in the given equation \[9e - 7 = 7e - 11\]
\[
   \Rightarrow 9( - 2) - 7 = 7( - 2) - 11 \\
   \Rightarrow - 18 - 7 = 14 - 11 \\
   \Rightarrow - 18 - 7 = - 14 - 11 \\
   \Rightarrow - 25 = - 25 \\
  LHS = RHS \\
 \]
Since values on both sides of the equation are equal hence verified that the solution is correct. Remember if the number is added we need to remove the number and if it is multiplied then we need to divide for removing the number by keeping the equation balanced.