### Chap 5 Algebra: 6 A.M. QUIZ (23 May 2010) (II)

Explain, with examples:
Which is larger: 2+n or 2n?

Note: This is a 6-mark question.

1. This comment has been removed by the author.

For example, if n's value is 1, 2+n would be larger than 2n as 2+n would have a value of 3 while 2n would only have a value of 2.

If the value of n were 2, 2+n and 2n would be of equal values as both would have a value of 4.

If the value of n were 3, 2n would be larger than 2+n as 2n would have a value of 6 while 2+n would only have a value of five. This also applies if the value of n is more than 3.

3. The answer depends on n, which means it varies.

If the value of n is 1 or below, 2+n would be larger than 2 x n.
Eg. n = 0.5,
2 + 0.5 = 2.5
2 x 0.5 = 1
2.5 is bigger than 1, which means 2+n is larger than 2 x n.

If the value of n is 2, 2 + n would be equal to 2 x n.
n = 2,
2 + 2 = 4
2 x 2 = 4
4 = 4, which means 2 + n would be equal to 2 x n.

If the value of n is more than 2, 2n would be larger than 2 +n.
eg. n = 2.2
2 + 2.2 = 4.2
2 x 2.2 = 4.4
4.4 is bigger than 4.2, which means that 2 x n is bigger than 2 + n.

JJ(:

4. 2n is larger then 2 + n

First, the answer will depend largely on the variable (n).
Second, the constant is 2 in both equations.

If the variable is 1 or 0 , 2n will be smaller then 2 +n since 2n= 2 x 1 or 2 x 0 and 2 +n is 2 + 1 or 2 + 0.

If the variable is 2 , there will be the same answer as 2 x 2= 4 and 2 + 2= 4

If the variable is more than 2, 2n will always be larger than 2 +n since there are 2 groups of the variable and 2 + 1 group is always smaller when the variable is more than 2.

5. 2n is larger.
Why?
2n is 2 x n, which is multiple, but 2+n is addition.
for example n=4
2+4=6, but 2x4=6

2+n can also be larger.
As long as the variable is no larger than the constant, 2+n is larger.
Example:

n=1:
2+1=3
2x1=2

n=(-1):
2+(-1)=1
2x(-1)=-2

Therefore, I can conclude that the answer cannot be defined as both answers are correct unless more information is provided like the value of n, the constant.

If n < 3, then 2+n is greater than 2n.

For example, n = 1,
then 2 + 1 = 3,
and 2 x 1 = 2,
from here we can see that 2+n is greater than 2n.

If n > 3, or n = 3, then 2n is greater than 2+n.

For example, n = 4,
then 2 + 4 = 6,
and 2 x 4 = 8,
from here we can see that 2n is greater than 2+n.

Therefore, we can only decide whether 2+n or 2n is greater when we are given the value of "n".

7. It depends on the value of the variable 'n'.
For example, if n=1.
2+1=3
2x1=2
This time, 2+n is greater than 2n.

For example, if n=2.
2+2=4
2x2=4
This time, 2+n and 2n is the same.

However, if n=3 and above, 2n will be greater than 2+n.

Hence, it depends on the value of 'n'.