The notation is as follows: Use parenthesis when we do NOT include the value, and square brackets when we DO include the value.
For example, (-3,4] means -2.99999 through 4. We do not include the -3 because of the parenthesis, and 4 is included because of the square bracket.
Now for your specific problem...
"y is at least 2" means that y has to have a lowest value of 2. In other words, the function needs to be greater or equal to 2.
Now we replace the 'y' in the given equation and replace the = sign with ≤, because the function needs to be greater or equal to 2.
2 ≤ 8 - (x+9) + 2x
Treat the inequality like an equals sign, so subtract 8 from both sides
-6 ≤ - (x+9) +2x
Distribute the negative on the right side
-6 ≤ -x -9 + 2x
Group like terms (the x's) on the right side
-6 ≤ -9 + x
Add 9 to both sides
3 ≤ x
Or if you prefer the x on the left side:
x ≥ 3
Interval notation for this is
[3,∞)
If you have any questions, please ask.
Nick S.
02/05/16