Find the range of values for z (will upload pic)

Question

anonymous · Answer

|dw:1424553552198:dw|

I got this range by putting z+11>4z-6 and got (17/3)>z.

Then I put z+11>0, got z>-11, and then 4z-6>0 and got z>(2/3) but Im not sure how to set them together to get the full range of values, since there are two different ones when I put it equal to zero.

jim_thompson5910 · Answer

I'm assuming this angle here is 122 degrees

|dw:1424563842042:dw|

jim_thompson5910 · Answer

since  z>-11 AND z> 2/3, this means that overall, z has to be greater than 2/3

We essentially ignore the z > -11 since something like z = -8 makes z > -11 true but makes z > 2/3 false. We have to make BOTH inequalities true here

so again, "z>-11 AND z> 2/3" condenses down to simply "z > 2/3"

jim_thompson5910 · Answer

we know that

z > 2/3 AND z < 17/3

that's the same as saying

2/3 < z AND z < 17/3

and those two combine to

2/3 < z < 17/3

jim_thompson5910 · Answer

2/3 < z < 17/3 says "z is some number between 2/3 and 17/3 excluding both endpoints"