Question

Twelve more than twice a certain number is six fewer than the three times the number. What is the number ?
(A) $ 6 $
(B) $ 12 $
(C) $ 16 $
(D) $ 18 $

Answer 1

Hint: In the given question, we are required to write an algebraic equation based on the information given to us. First, we break down the information given to us to try and identify what the algebraic equation must look like. You should always know what you are dealing with. A sum means that you are adding something, so you are going to use the $ + $ sign and so on. Then, after framing a mathematical equation, we try to solve it by using the method of transposition.

Complete step-by-step answer:
The statement “twelve more than twice a certain number” means first multiplying a number by $ 2 $ and then adding $ 12 $ to the product.
So, let us assume that the number is x.
Then, we get the algebraic expression $ \left( {2x + 12} \right) $ .
Now, we are given that the expression is six fewer than the three times the number assumed.
Now, we know that three times the number is $ 3x $ .
So, framing the mathematical equation, we get,
 $ \Rightarrow \left( {2x + 12} \right) = \left( {3x - 6} \right) $
Now, we have to solve the above equation using the transpositions and simplification methods.
Shifting all the terms consisting x to the right side of the equation and all the constants to the left side, we get,
 $ \Rightarrow 12 + 6 = 3x - 2x $
Simplifying the expression further, we get,
 $ \Rightarrow x = 18 $
So, the value of x is $ 18 $ .
Hence, option (D) is correct.
So, the correct answer is “Option D”.

Note: An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.
An equation will always use an equivalent $ \left( = \right) $ operator between the two terms. Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding value of the required parameter.