# 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

Verified

283.8k+ views

**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.

Recently Updated Pages

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is 1 divided by 0 class 8 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Convert compound sentence to simple sentence He is class 10 english CBSE

India lies between latitudes and longitudes class 12 social science CBSE

Why are rivers important for the countrys economy class 12 social science CBSE

Distinguish between Khadar and Bhangar class 9 social science CBSE