Question

Identify all the roots for the equation $ 3\left| {W - 14} \right| - 6 = 21 $
 $ \left( a \right){\text{ 19}} $
 $ \left( b \right){\text{ 23}} $
 $ \left( c \right){\text{ 5 and 23}} $
 $ \left( d \right){\text{ 9 and 19}} $

Answer 1

Hint: So for solving this type of question we just have to find the values by moving the terms to the one side. Here in this question, we will split the equation into two cases, one will be positive and the other will be negative cases. And solving the equation we will get the solution.

Complete step-by-step answer:
So we have the equation given as $ 3\left| {W - 14} \right| - 6 = 21 $
On moving another term to the right side and adding it, we get
 $ \Rightarrow 3\left| {W - 14} \right| = 27 $
Now the bars will be cleared by splitting the equation into two cases.
For the negative case, the equation will be
 $ \Rightarrow - 3\left( {W - 14} \right) $
For positive case, the equation will be
 $ \Rightarrow 3\left( {W - 14} \right) $
So on solving the negative case, we have the equation as
 $ \Rightarrow - 3\left( {W - 14} \right) = 27 $
On multiplying, we get
 $ \Rightarrow - 3W + 42 = 27 $
So on rearranging the equation and adding it, we get
 $ \Rightarrow - 3W = - 15 $
On dividing it by $ - 3 $ both the sides, we get
 $ \Rightarrow W = 5 $
Which will be the solution for the negative case.
So on solving the positive case, we have the equation as
 $ \Rightarrow 3\left( {W - 14} \right) = 27 $
On multiplying, we get
 $ \Rightarrow 3W - 42 = 27 $
So on rearranging the equation and adding it, we get
 $ \Rightarrow 3W = 69 $
On dividing it by $ 3 $ both the sides, we get
 $ \Rightarrow W = 23 $
Which will be the solution for the positive case.
Therefore, on wrapping up the solution we have $ W = 5 , 23 $
So, the correct answer is “Option C”.

Note: For solving this type of question, there is not much need for calculation. The only concept used in this is while solving the question of an absolute bar we should first split the equation into two cases which will be positive and negative, and then solve them respectively.