Question

Which inequality is represented by the graph below?

Answer 1

can you help me with this please? @jim_thompson5910

Answer 2

where is the circle located?

Answer 3

the -1 @jim_thompson5910

Answer 4

so the answer will look like this

x ? -1

where some inequality sign will replace the question mark

Answer 5

is the shading to the left? or to the right?

Answer 6

to the right @jim_thompson5910

Answer 7

so the inequality sign is either > or ≥

Answer 8

last question to ask yourself: is the circle filled in? or is it hollow?

Answer 9

the one on the -1? @jim_thompson5910

Answer 10

yes, the circle at -1

Answer 11

its hollow @jim_thompson5910

Answer 12

so we use the inequality sign >

so in the end, the inequality is

x > -1

Answer 13

but why that sign? @jim_thompson5910

Answer 14

Rules:

if you have a > sign, then you shade to the right of an open circle
if you have a < sign, then you shade to the left of an open circle


if you have a ≥ sign, then you shade to the right of a closed/filled in circle
if you have a ≤ sign, then you shade to the left of a closed/filled in circle

Answer 15

x > -1 basically says: shade the region that has all the numbers greater than -1 (ie the region that has 0, 1, 2, 3, ...) but do NOT include -1 in the shaded region

Answer 16

so that's why you shade to the right of an open circle with x > -1

Answer 17

ohhhh i get it :) so the answer would be x>-1? @jim_thompson5910

Answer 18

you got it

Answer 19

So when dealing with these types of problems, have those 4 rules on paper or in your head and work your way backwards from them

Answer 20

Thank you so much :) @jim_thompson5910

Answer 21

you're welcome