The total number of choices Jalen has is six
Answer:
The answer is -4
Step-by-step explanation:
-2x-6<=1
-2(-4)-6<=1
8-6<=1
2<=1 which is False
-2x-6<=1
-2(-3)-6<=1
6-6<=1
0<=1 which is True
-2x-6<=1
-2(-2)-6<=1
4-6<=1
-2<=1 which is True
-2x-6<=1
-2(-1)-6<=1
2-6<=1
-4<=1 which is True
A function

is periodic if there is some constant

such that

for all

in the domain of

. Then

is the "period" of

.
Example:
If

, then we have

, and so

is periodic with period

.
It gets a bit more complicated for a function like yours. We're looking for

such that

Expanding on the left, you have

and

It follows that the following must be satisfied:

The first two equations are satisfied whenever

, or more generally, when

and

(i.e. any multiple of 4).
The second two are satisfied whenever

, and more generally when

with

(any multiple of 10/7).
It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when

is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.
Let's verify:


More generally, it can be shown that

is periodic with period

.
9. Let x equal the number
Two less than a number is
x - 2
Is more than 15 is
> 15
Put them together for
x-2 > 15
Now solve
x-2 > 15
x > 17
10. Let x equal a number
Seven more than a number is
x+ 7
Is less than or equal to 27 is
<= 27
Put them together for
x + 7 <= 27
Now solve
x+ 7 <= 27
x <= 20