Answer:
Part 1) [tex]30< 6x< 48[/tex]
Part 2) [tex]-80< -10x< -50[/tex]
Part 3) [tex]0<x-5< 3[/tex]
Part 4) [tex]17< 3x+2< 26[/tex]
Step-by-step explanation:
we know that
[tex]5< x< 8[/tex]
The solution for x is the interval ----> (5,8)
All real numbers greater than 5 and less than 8
Part 1) Find all possible values of the expression 6x
so
For x < 8
The expression value is 6x < (6)(8) -----> 6x < 48
For x > 5
The expression value is 6x > (6)(5) -----> 6x > 30
therefore
[tex]30< 6x< 48[/tex]
Part 2) Find all possible values of the expression -10x
so
For x < 8
The expression value is -10x > (-10)(8) -----> -10x > -80
For x > 5
The expression value is -10x < (-10)(5) -----> -10x < -50
therefore
[tex]-80< -10x< -50[/tex]
Part 3) Find all possible values of the expression x-5
so
For x < 8
The expression value is x-5 < 8-5 -----> x-5 < 3
For x > 5
The expression value is x-5 > 5-5 -----> x-5 > 0
therefore
[tex]0<x-5< 3[/tex]
Part 4) Find all possible values of the expression 3x+2
so
For x < 8
The expression value is 3x+2 < 3(8)+2 -----> 3x+2 < 26
For x > 5
The expression value is 3x+2 > 3(5)+2 -----> 3x+2 > 17
therefore
[tex]17< 3x+2< 26[/tex]
