Chapter 4: Algebra... Which is larger in magnitude?

Which is larger in magnitude?

5 + n or  5n

This question is compulsory.

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4. It depends on the value of n. If for example, n is 10, 5 + n would be 15, while 5n would be 50.Thus, 5n would be greater.
But, if n is 0.2, 5+n would be 5.2, while 5n would be 1.Thus, 5+n would then be greater.

5. 5n as 5+n is n + 5 but 5n is n x n x n x n x n.

6. 5n as 5+n is smaller than 5 x n cuz 5n=5 x n but 5 + n is 5 + n. idk how to explain ps.
EG. let n be 10. 5+10=15 but 5 x 10 = 50
The exception is if n is a negative number.
EG: if n is -1. 5+(-1)=4 but 5 x (-1) is -5 and 4 is bigger than -5

7. It depends on what n is, because if n is 0, 5+n would be more than 5n. Whereas if n was 10, 5+n would be less than 5n. Therefore, it is not possible to tell if 5+n is more than 5n or not.

8. Depends.

e.g.
n=10
5+10=15
5*10=50

e.g.
n=(-10)
5+(-10)=(-5)
5*(-10)=(-50)

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10. It depends. This is because that in this case, if you let n as 1 , then 5+1=6, while 5x1=5, then 5+n is bigger. But if n is 10, then 5+10=15, and 5x10=50 then 5n is bigger.

11. It depends.

If n ≤ 1, 5+n (e.g. 5+1 = 6) will be greater than 5n (e.g. 5 * 1 = 5) // 5 + n (e.g 5 + 0 = 5) will be greater than (e.g. 5 * 0 = 0)
If n > 1, 5n (e.g. 5 * 2 = 10) will be greater than 5+n (e.g. 5 + 2 =7)

1. 5n = 5+n
4n = 5
n = 1.25

12. It depends. 5N could be bigger, or 5+N is bigger

Example:

Let N be 1

So 5N is 5x1
=5
and 5+N is 5+1
=6

Or,

let N be 4

so 5N=5x4
=20

and 5+N=5+4
=9

13. 5n would always be larger than 5+n if "n" is more than 1. If "n" is 1, than 5n would be smaller than 5+n.

Example: n=1
5*1=5
5+1=6 (5+n is larger than 5n)

Example 2: n=10
5*10=50
5+10+15 (5n is larger than 5+n in this case, where "n" is more than 1)

1. 2) If "n" is 0, then 5n would be smaller than 5+n.

Example: n=1
5*0=0
5+0=5

2. If 5n<5+n
= n<1.25

If 5n>5+n
"n" must be more than 1.25.
If "n" is 1.25, the two numbers are the same.

14. It can be bigger or smaller.
1)n=2
5n=5x2=10
5+n=5+2=7
So, 5n is bigger.

2)n=-2
5n=5x-2=-10
5+n=5+(-2)=3
So, 5+n is bigger.

15. 5n is larger in magnitude than 5+n. For example, let n be 3 and 5+n would be equal to 5+3=8 and thus, 5n would be equal to 5x3=15 and thus we can conclude that 5n is larger in magnitude than 5+n as 5n is multiplication and 5+n is addition.

16. It depends on what is n because if n is 5,then first sum will be 10. The second sum will be 25.
However if n is 1 then the first sum will be 6 and the second sum will be 5.

17. It depends on what is n because if n is 5,then first sum will be 10. The second sum will be 25.
However if n is 1 then the first sum will be 6 and the second sum will be 5.

18. It depends on what is the value of n.

E.g. N=1
5+1=6
1*5=5
In this case 5+n is larger than 5n

E.g N=2
5+2=7
5*2=10
In this case 5n is larger than 5+n

19. if n is 1 or a smaller number(can be negative number too), 5+n would be larger than 5n if n is 1 ( 5+1=6, 5x1=5 ) but if n is above 1, 5n will be larger than 5+n (5+2=7,5x2=10)

20. 5n is greater than 5+n for most cases for positive whole numbers for example (n=10);(5+10 =15)<(5x10=50)
But if 'n' is a negative number , 0 or a decimal, 5+n is grater than 5n (5+0=5)>(5x0=0)

21. If n is a positive number, 5n is larger than 5+n. eg. n is 3, 5+3=8, 5x3=15. If n is a negative number or 1, 5n will be smaller than 5+n. eg. 5x-2=-10, 5+-2=3. So we can't tell which is bigger.

1. If n is a negative number, 1 or 0*

22. It depends on the value of n.If n is a positive a number and it is a whole number above 1,5n will be more than 5+n.But when n is negative or decimal below 1 5+n will have a larger value than 5n

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24. Let n=6,
5+n=5+6
5n=5x6

Thus, it is obvious that 5n is greater than 5+n, assuming n=natural number and rational number. (n >1)

1. 5xn=5+n
5xn-n=5
4n=5
n=5/4
n=1.25

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26. 5+n will be larger than 5n if n=1 eg.[5+1>5(1)].
5n will be larger 5+n if it is greater than 1.eg.[5+10<5(10)].
If n is a negative no. or 0, 5+n will be greater than 5n [5+(-1)>5(-1)]

27. It depends on whether n is a positive or a negative number. Whether it is a whole number or a decimal/fraction. If it is a positive and a whole number then 5n will have a larger magnitude than 5+n but if it is a negative and decimal/fraction number then 5+n will have a larger magnitude than 5n.

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29. If 5n = 5 + n
5n - n = 5 + n - n
4n = 5
n = 5/4
=1.25
=1 1/4

So, if n > 5 + n
n > 1.25

And if n < 5 +n
n < 5 + n