Question

Which of the following statement do not hold in solving the equation 15 + 3 x = 3?
A) 3 x = 3 – 15
B) 15 – 3 = – 3 x
C) 15 + $\dfrac{{3x}}{3}$= 3
D) $\dfrac{{15}}{3} + \dfrac{{3x}}{3} = \dfrac{3}{3}$

Answer 1

Hint: We will check the plausibility of each option to see if it holds or not in solving the given equation: 15 + 3 x = 3. We will see if the options can reform into the given equation. Or we can check by putting the values of the options in the given equation to see if they are true or not.

Complete step by step solution: We are given the equation: 15 + 3 x = 3. We will see that if the given options hold true individually or not.
Option(A) is 3 x = 3 – 15.
Upon putting the value of 3 x in the given equation 15 + 3 x = 3, we get
$ \Rightarrow $15 + $\left( {3 - 15} \right)$= 3
$ \Rightarrow $15 + 3 – 15 – 3 = 0
$ \Rightarrow $0 = 0
Hence, option (A) holds for the given equation.
Option (B) is 15 – 3 = – 3 x. it can be re – written upon multiplying both sides by -1 as – 15 + 3 = 3 x.
Upon putting the value of 3 x in the given equation, we get
$ \Rightarrow $15 +( – 15 + 3) = 3
$ \Rightarrow $15 – 15 + 3 – 3 = 0
$ \Rightarrow $0=0
Hence, option (B) holds true.
Option(C) is 15 + $\dfrac{{3x}}{3}$= 3. We can re – write this equation as 15 + 1x = 3.
By observation, we can say that this option cannot hold true for the given equation: 15 + 3 x = 3 as the coefficient of the x in the given equation is 3 but, in the option, it is 1.
Hence, option (C) does not hold for the given equation.
Option(D) is $\dfrac{{15}}{3} + \dfrac{{3x}}{3} = \dfrac{3}{3}$ . we can also write this equation as 15 + 3x = 3.
We can see that this equation reformed into the given equation, and hence, it will hold true.

Therefore, option(C) is the answer.

Note: In such questions, you can easily find the correct answer but you need to take care of the method used. you can also solve this equation by considering the given equation: 15 + 3x = 3 and then reforming it into the options but you had to spend more time using that method.