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;

 

D. the relationship cannot be determined from the information given.

 

Column A     Column B

 

$\text{x}+13$                 $\text{x}+14$

Step-by-Step Solution

Answer

The quantity in Column B is greater. So, the correct option is B.

Step 1 - Consider the two quantities.

The quantity in column A is:

$x+13$

The quantity in column B is:

$x+14$

Step 2 - Evaluate the two quantities.

Here, the value of x or  type of number x can be is not mentioned.

 

Suppose x is a positive number then the quantity in column A is less than quantity in column B. Since any positive interger added to a positive number the resultant value will be a positive number and as 13 is less than 14. So, $x+13<x+14$.

 

Now, suppose x is a negative number then the quantity in column A is greater than quantity in column B. 

For example, 

Let $x=-2$, then

 

$\begin{array}{c}x+13=-2+13\\ =11\end{array}$

And 

 

$\begin{array}{c}x+14=-2+14\\ =12\end{array}$

 

Here, $x+13<x+14$. This is the case for all negative numbers of x.

Step 3 - State the conclusion.

Thus from above steps the quantity in Column B is greater. So, the correct option is B.