Question

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

Answer 1

Answer:

6x: 30<6x<48

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

x-5: 0<x-5<3

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

Answer 2

Answer:

Part 1) $30< 6x< 48$

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

Part 3) $0$

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

Step-by-step 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

$0$

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

$17< 3x+2< 26$