Q20. - Algebra 2

Question

 Compare the quantity in Column A and the quantity in Column B. Then determine whether:

(A) The quantity in Column A is greater,

(B) The quantity in Column B is greater,

(C) The two quantities are equal, or

(D) The relationship cannot be determined from the information given.

 

20. $3x+12=5x-3$

Column A: $2x$.

 

Column B: $9$.

Step-by-Step Solution

Answer

The correct option is (D), the other options are wrong because one cannot determine the relationship between the given quantities from the given information.

Step 1 – Solve the given equation.

Solve:

    $\begin{array}{d}3x+12=5x-3\\ 3x+12-3x=5x-3-3x\\ 12=2x-3\\ 12+3=2x-3+3\\ 15=2x\end{array}$

Step 3 – Check whether the option A is correct or incorrect.

The value of the quantity in column A is 2x and the quantity in column B is 9.

 

One cannot determine that the quantity in column A is greater.

So, the option A is incorrect.

Step 3 – Check whether the option B is correct or incorrect.

The value of the quantity in column A is 2x and the quantity in column B is 9.

 

One cannot determine that the quantity in column B is greater.

So, the option B is incorrect.

Step 4 – Check whether the option C is correct or incorrect.

The value of the quantity in column A is 2x and the quantity in column B is 9.

 

Here the values of the two quantities in column A and column B are two different values, from the given equation we get the result 2x=15.o

So, the option C is incorrect.

Step 5 – Check whether the option C is correct or incorrect.

The value of the quantity in column A is 2x and the quantity in column B is 9.

 

Here the values of the two quantities in column A and column B are two different values, from the given equation we get the result 2x=15.o

So, one cannot determine a relationship between the quantities.

So, the option D is correct.

 

Hence, the correct option is (D), and the other options are wrong because, one cannot determine the relationship between the given quantities from the given information.