Question

A function is given by the formula y= −1.5x + 7.5 . For what value(s) of x is: y>0

and
A function is given by the formula y= −1.5x + 7.5 . For what value(s) of x is: y<0

Answer 1

a)
`(5, \infty)`

b)
`(-\infty,5)`

Explanation:

We are given the following information in the question:

a)

`y = -1.5x + 7.5\\y > 0\\\Rightarrow -1.5x + 7.5 > 0\\-1.5x > -7.5\\x > \displaystyle(-7.5)/(-1.5) = 5\\\\x > 5\\x \in (5, \infty)`

For y to be greater than zero x should belong in the interval
`(5, \infty)`

b)

`y = -1.5x + 7.5\\y < 0\\\Rightarrow -1.5x + 7.5 < 0\\-1.5x < -7.5\\x < \displaystyle(-7.5)/(-1.5) = 5\\\\x < 5\\x \in (-\infty,5)`

For y to be less than zero x should belong in the interval
`(-\infty,5)`

Answer 2

Part 1)
`x < 5` (all real numbers less than 5)

Part 2)
`x > 5` (all real numbers greater than 5)

Explanation:

Part 1) we have

`y=-1.5x+7.5`

Solve the inequality For y > 0

`-1.5x+7.5> 0`

Subtract 7.5 both sides

`-1.5x+7.5-7.5> 0-7.5`

`-1.5x> -7.5`

Multiply by -1 both sides

`1.5x < 7.5`

Divide by 1.5 both sides

`x < 7.5/1.5`

`x < 5`

Part 2) we have

`y=-1.5x+7.5`

Solve the inequality For y < 0

`-1.5x+7.5< 0`

Subtract 7.5 both sides

`-1.5x+7.5-7.5< 0-7.5`

`-1.5x< -7.5`

Multiply by -1 both sides

`1.5x > 7.5`

Divide by 1.5 both sides

`x > 7.5/1.5`

`x > 5`