Question

Solve \[8v = 2(4v + 2)?\]

Answer 1

Hint: To solve the algebraic equation we need to simplify the equation. Then, by combining like-term we can proceed to solve. In algebraic linear equation we may get three types of solutions,
 (i) Unique solution
(ii) Infinite solution
(iii) No solution
Hence, whenever we get a question related to finding the solution of a given equation , the answer must match with the above three cases.

Complete step by step solution:
We need to evaluate:- \[8v = 2(4v + 2)\]
\[\therefore \] By using, distributive property to RHS of the given equation; we get.
=> \[8v = 8v + 4\]
Now, by subtracting \['8v'\] from both sides of the equation, we get:-
\[\Rightarrow 8v - 8v = 8v + 4 - 8v\]
Now, cancelling common terms from both the sides, we get:-
\[\Rightarrow 0 = 4\];which is not at all possible
And we know, \[0 \ne 4\]
Since, \[0\] is not equal to \[4\], the answer is ‘no solution’ to this problem is a null set, i.e; \[\{ \phi \} \].
Thus, we can interpret that, there is no value of \['v'\] for which L.H.S. of the equation will be equal to R.H.S. of the equation.

Note: Always remember
A linear equation can have three types of solution as we have discussed :-
• Unique solution - One value
• Infinite solution - Uncountable values
•No solution - Not a finite answer
The answer must match with the above three cases.