Question

Find the solution of\[ - 2 = - \left( {n - 8} \right)\].

Answer 1

Hint:Whenever there are questions on brackets, the first thing that should be done is expansion of brackets because after expansions only the proper sign can be known so that calculations can be one accurately. The aim is to find out the value of an unknown variable in the equation. For easy calculations like terms should be taken one side.

Complete step by step solution:
First expanding the terms within parenthesis on the right side of the equation by multiplying each term within the parenthesis or the bracket by the negative sign we have, \[ - 2 = - n + 8\]
Since, whenever a negative is multiplied by positive the result is always negative and similarly whenever a negative is multiplied by another negative then the result is always positive.
Now, taking all the like terms on the Left Hand Side (LHS) we have,
\[ \Rightarrow n = 2 + 8\]
Whenever a number is taken from LHS to RHS or from RHS to LHS then always there is a change in sign. That is when “n” is taken from LHS to RHS it is changed to a positive sign. Also when 2 is taken from RHS to LHS it is changed to a positive sign.
Hence, we have
\[ \Rightarrow n = 10\]
Therefore, the solution of \[ - 2 = - \left( {n - 8} \right)\]is\[n = 10\].

Note: Sign conversions should be taken care of always. LHS to RHS or vice versa the sign changes from positive to negative and negative to positive. Solutions can only be done if like terms are at one side otherwise unlike terms cannot be added or subtracted. If there is a bracket then that should be expanded.