qwertylol12345
contestada

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

Respuesta :

calculista

Answer:

Part 1) [tex]x < 5[/tex]  (all real numbers less than 5)

Part 2) [tex]x > 5[/tex]  (all real numbers greater than 5)

Step-by-step explanation:

Part 1) we have

[tex]y=-1.5x+7.5[/tex]

Solve the inequality For y > 0

[tex]-1.5x+7.5> 0[/tex]

Subtract 7.5 both sides

[tex]-1.5x+7.5-7.5> 0-7.5[/tex]

[tex]-1.5x> -7.5[/tex]

Multiply by -1 both sides

[tex]1.5x < 7.5[/tex]

Divide by 1.5 both sides

[tex]x < 7.5/1.5[/tex]

[tex]x < 5[/tex]

Part 2) we have

[tex]y=-1.5x+7.5[/tex]

Solve the inequality For y < 0

[tex]-1.5x+7.5< 0[/tex]

Subtract 7.5 both sides

[tex]-1.5x+7.5-7.5< 0-7.5[/tex]

[tex]-1.5x< -7.5[/tex]

Multiply by -1 both sides

[tex]1.5x > 7.5[/tex]

Divide by 1.5 both sides

[tex]x > 7.5/1.5[/tex]

[tex]x > 5[/tex]

Answer:

a)[tex](5, \infty)[/tex]

b)[tex](-\infty,5)[/tex]      

Step-by-step explanation:

We are given the following information in the question:

a)

[tex]y = -1.5x + 7.5\\y > 0\\\Rightarrow -1.5x + 7.5 > 0\\-1.5x > -7.5\\x > \displaystyle\frac{-7.5}{-1.5} = 5\\\\x > 5\\x \in (5, \infty)[/tex]

For y to be greater than zero x should belong in the interval [tex](5, \infty)[/tex]

b)

[tex]y = -1.5x + 7.5\\y < 0\\\Rightarrow -1.5x + 7.5 < 0\\-1.5x < -7.5\\x < \displaystyle\frac{-7.5}{-1.5} = 5\\\\x < 5\\x \in (-\infty,5)[/tex]

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

Otras preguntas