Interval notation

Question

If someone could help me, it would be greatly appreciated. If you could let me know how you do it too, that would be very helpful. Thanks!

Use interval notation to represent all values of x satisfying the given conditions: 

y=8-(x+9)+2x and y is at least 2

Answer 1

Y is at least 2, that is the hint. It means

 

8-(x+9)+2x ≥2,  now we need to simplify the left side:

 

8-x-9+2x ≥2

 

-1 + x ≥ 2

 

add 1 on both sides:

 

x ≥ 3, this is the answer, but we need to write it in interval notation:

 

[3, ∞ )

Answer 2

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.