If $-3\le x+5 \le 8$ and $x$ is an integer, what is the sum of all the possible solutions?

-30

Step-by-step explanation:

The integers are the whole numbers and the opposite of the whole numbers.

That is {...,-3,-2,-1,0,1,2,3,...} is the set of integers.

If it is a number you count with or the opposite of a number you count with it or 0, then it is an integer.

So we need to solve the inequality first, and then just say all the integers included in that compound inequality. Last step is to add since it is asking for the sum of those integers.

Let's do this.

Subtract 5 on all sides:

Simplify all sides:

This inequality includes all numbers between -8 and 3, and both include -8 and 3 because of the equal part on both of the inequality parts.

So we have -8,-7,-6,-5,-4,-3,-2,-1,0,1,2, and 3 are the integer solutions of this inequality.

Let's add them. I'm going to put opposites together because I know they will zero out.

So I have this:

-8+-7+-6+-5+-4+-3+-2+-1+0+1+2+3

-8+-7+-6+-5+-4+(-3+3)+(-2+2)+(-1+1)+0

-8+-7+-6+-5+-4+0       +0        +0     +0

-8+-7+-6+-5+-4

-(8+7+6+5+4)

-([8+7]+[6+5]+4)

-([15]+[11]+4)

-(15+11+4)

-([15+11]+4)

-([26]+4)

-(26+4)

-(30)

-30

answer: a clock

step-by-step explanation:

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!