Question

x - 1 less than or equal to 7
2x greater than or equal to 22

what could these looks like on a number line, with a closed or open circle ?

Answer 1

x -1 < = 7

to "simplify" add +1 to both sides
x -1 + 1 < = 7 + 1
can you simplify both sides?

Answer 2

7 + 1 = 8.
x = 8.

Answer 3

ok but you should keep the "relation" < = (which means less than or equal) (you could use \( \le\) )

x < = 8

x could be equal to 8, so put a filled in dot at 8
then show the numbers less than 8 (which side of 8 is that on a number line?

Answer 4

to the left, yes?

Answer 5

yes, to the left. a solid dot at 8 and an arrow pointing to the left (toward numbers smaller than 8)

Answer 6

is this a separate problem:
2x greater than or equal to 22

2x > = 22

Answer 7

okay.
so x could be 11, yes?

Answer 8

yes

Answer 9

I would divide both sides by 2 to get
x >= 11

solid dot at 11 (because x could = 11)
and an arrow pointing to numbers bigger than 11
(x can be 11 or bigger)

Answer 10

to the right side, because the numbers are larger, yes?

thank you very much!

Answer 11

good job

Answer 12

the only tricky part is when you write
>
the "big end" is next to the bigger number
and the "small, pointy end" is next to the smaller number
so
2 > 1
or
1 < 2
both mean the same thing, and both are true.

Answer 13

cool, i didn't know that! thank you :)