Answer:
Problem 1)
[tex]-11<x<-4[/tex]
Sample value is -6.
Problem 2:
[tex]3<y<9[/tex]
Sample value is 6.
Problem 3:
[tex]5<z<6[/tex]
Sample value is 5.5.
Step-by-step explanation:
We can write inequalities to represent each situation.
Problem 1)
(11 + x) is positive and (4 + x) is negative. In other words:
[tex]11+x>0\text{ and } 4+x<0[/tex]
Solving for x yields:
[tex]x>-11\text{ and } x<-4[/tex]
Combining them:
[tex]-11<x<-4[/tex]
Any values that satisfy this inequality will work.
An example will be -6.
Problem 2)
(-3 + y) is positive and (-9 + y) is negative. Hence:
[tex]-3+y>0\text{ and } -9+y<0[/tex]
Solving for y yields:
[tex]y>3\text{ and } y<9[/tex]
So:
[tex]3<y<9[/tex]
A sample value will be 6.
Problem 3)
(-5 + z) is positive and (-6 + z) is negative. Hence:
[tex]-5+z>0\text{ and } -6+z<0[/tex]
Solving for z yields:
[tex]z>5\text{ and } z<6[/tex]
So:
[tex]5<z<6[/tex]
A sample value will be 5.5.
Answer:
1) you can choose: -5, -6, -7, -8, -9, or -10
Step-by-step explanation:
If you subtract 11 + -5 through -10 you have a positive number. If you subtract 4 + -5 through -10 you have a negative number.
