2. x is less than or equal to -5
So x could be -5, -6, -7, -8, -9, -10.....and so on
3. 16 is less than x, or x is greater than 16
So x could be any number greater than 16
4. x + 9 > 21; x = 10
Since you know "x", plug it in
x + 9 > 21
10 + 9 > 21
19 > 21
It is NOT a solution because 19 is NOT greater than 21
5. 3x < 45; x = 20
Plug in x
3x < 45
3(20) < 45
60 < 45
It is NOT a solution because 60 is NOT less than 45
6. 2x - 15 ≥ 5; x = 10
Plug in x
2x - 15 ≥ 5
2(10) - 15 ≥ 5
20 - 15 ≥ 5
5 ≥ 5
It IS a solution because 5 IS greater than or equal to 5
7. You see how the dot is filled in or not filled in? The dot is filled in when the sign is ≤ or ≥ ("less/greater than or equal to") The dot is NOT filled in when the sign is < or >.
Since the arrow is going to the left of 6, that means that "x" is any number less than 6
x < 6
8. The dot is filled in and the arrow is going to the left of -3, that means "x" is less than or equal -3
x ≤ -3
9. The dot is not filled in, and the arrow is going to the right of 0, that means that "x" is any number greater than 0
x > 0
(I'll update problems 10-12 in a few minutes)