Question

Choose the correct description of the graph of the compound inequality

x - 3 < -9 or x + 5 greater than or equal to 10

A. A number line with an open circle on -6, shading to the left, and a closed circle on 5, shading to the right.

B. A number line with a closed circle on -6, shading to the left, and an open circle on 5, shading to the right.

C. A number line with an open circle on -6, a closed circle on 5, and shading in between.

D. A number line with a closed circle on -6, an open on circle on 5, and shading in between.

Answer 1

Okay the first step would be to solve these inequalities for x
So if you did that, what inequalities would you get?

I won;t tell you the answer, but I will help you to solve it :)

Answer 2

I honestly have no clue how to go about it... I don't understand inequalities at all. :s

Answer 3

x - 3 < 9 x +5 >= 10
x < 9 + 3 x >= 10 - 5
x < 12 x >= 5

so we have x is less then 12 and greater then or equal to 5
quick lesson.....when it is less then, shading goes to the left. When it is greater then, shading goes to the right. It will be a closed circle only if there is an equal sign involved. If there is no equal sign, it will be an open circle.
Can you now find the answer ?

Answer 4

Great answer from @texaschic101 , do you understand it though @sammmm ?

Answer 5

you solve inequalities just like you solve equations except inequalities have some rules. One rule is that when you divide or multiply by a negative, the sign changes

Answer 6

So, x < 12, the shading would go to the left, with an open circle?

Answer 7

correct

Answer 8

So the answer is A?

Answer 9

yes

Answer 10

@texaschic101 okay, awesome, thank you so much! can you work out some more with me?

Answer 11

wait...no

Answer 12

no?

Answer 13

I did the first inequality wrong....
x - 3 < -9 (I forgot the - in front of the nine)
x < -9 + 3
x < -6

Answer 14

so the shading would go to the right...

Answer 15

lol...the answer is still A...
if it is less then shading still goes to the left

Answer 16

did I just confuse you ?

Answer 17

No I think I understand, it's just a bit confusing...

For this one...
Choose the correct description of the graph of the inequality -x less than or greater to 3.
If it's less than would the shading goes to the left with a closed circle?

Answer 18

-x < = 3 (-x is the same as -1x)
we do not want x to be negative, therefore, we will multiply the inequality by -1
making the inequality x >= -3
Here comes the rule : dividing/multiplying by a negative, changes the sign.

By the way, I am just assuming the problem means less then or equal, and not less then or greater.

So, if x is greater then or equal to a -3, then what does your graph look like ?

Answer 19

closed circle, shading to the right?

Answer 20

BINGO...you got it :)

Answer 21

just don't forget that rule.....it is important :)

Answer 22

yay! I think I will be okay... if I need help, I know to come to you. thank you so much!

Answer 23

your very welcome....sorry about the mess up on the first problem :)