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-1/9t>or equal to 7

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Hi Laura;
I think you do not understand the difference between...
> and <
 
When I was in sixth grade, the way we remembered this is, the alligator is going to eat the bigger one.
 
≤ ≥
The alligator works the same way, except it may also eat something equal to that on the other side of the sign.  It is fussy, but not that fussy.
 
-1/9t≤7
I assume this is...
(-1/9)t≤7
Let's multiply both sides by -9
(-9)(-1/9)t≥(7)(-9)
Because we are multiplying by a negative number on both sides, the sign must switch--in response to negativity, the alligator is changing direction.
And because a negative number multiplied by another negative number renders a positive result...
And because a positive number multiplied by a negative number renders a negative result...
t≥-63
 
Another number greater than or equal to -63 resolves this and satisfies the alligator.
 
Unless I misunderstood you and the equation is...
-1/(9t)≤7
Let's multiply both sides by t...
(t)[-1/(9t)]≤7(t)
-1/9≤7t
Let's multiply both sides by 1/7...
(1/7)(-1/9)≤(7t)(1/7)
-1/63≤t