Question

What is "ten is at least the product of a number h and 5." In a problem?

Answer 1

Start with the product of h and 5.
How do you represent that?

Answer 2

h times 5 as h5?

Answer 3

In theory, that should be correct, but everyone writes it as 5h.
We usually write the number before the variables.

Answer 4

What does "10 at least" mean?

Answer 5

Now the problem is to write this mathematically.
10 is at least 5h

Answer 6

Yes that's right, I did it incorrectly.

Answer 7

Ok.. So then at least would mean < or >

Answer 8

You know the symbols:

\( =\) means "is equal to"
\(\lt\) means "is less than"
\(\gt\) means "is greater than"
\(\le\) means "is less than or equal to"
\(\ge\) means "is greater than or equal to"

We need to use on of the those symbols to compare 10 and 5h.
There is no symbol that is usually described as meaning "is at least", but one of the symbols above means just that.

Answer 9

If I said I have at least 10 coins.
Can you name some numbers of coins I could have?

Answer 10

What is the smallest number of coins I have if I have at least 10 coins?

Answer 11

Right, I just wonder what "at least" would be.

Answer 12

You could have dimes

Answer 13

1 dime.

Answer 14

I have only dimes.
I have at least 10 dimes.
What is the smallest number of dimes I can have?

Answer 15

Nickels?

Answer 16

Forget coins.
I only have marbles in my pocket.
I have at least 10 marbles in my pocket.
What is the smallest number of marbles that I can have?

Answer 17

If I have at least 10 marbles, can I possibly have only 5 marbles?

Answer 18

No because you can only have 10 marbles or more.

Answer 19

Exactly.
At least means that number or more.
Very good.
Now we need to see which of the symbols I listed above can be used to mean at least.

Answer 20

The smallest number you can have is 10.

Answer 21

10 is at least 5h
means
10 is equal to 5h, or 10 is greater than 5h

Answer 22

Which symbol means
greater than or equal to?

Answer 23

Ok, I get it. So it would be 10>=5h

Answer 24

Ten is greater than or equal to 5h.

Answer 25

Correct.

Answer 26

at least = greater than or equal to
at most = less than or equal to

Answer 27

Thanks!