Question

It is known that 5< x< 8. find all possible values of the expression, 6x, -10x,x-5,3x+2

Answer 1

6x: 30<6x<48

-10x: -80<-10x<-50

x-5: 0<x-5<3

3x+2: 17<3x+2<26

Answer 2

Part 1)
`30< 6x< 48`

Part 2)
`-80< -10x< -50`

Part 3)
`0<x-5< 3`

Part 4)
`17< 3x+2< 26`

Explanation:

we know that

`5< x< 8`

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

`30< 6x< 48`

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

`-80< -10x< -50`

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

`0<x-5< 3`

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

`17< 3x+2< 26`