Question

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

Answer 1

Answer:

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

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

Step-by-step 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

$x > 7.5/1.5$

$x > 5$

Answer 2

Answer:

a)$(5, \infty)$

b)$(-\infty,5)$      

Step-by-step explanation:

We are given the following information in the question:

a)

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

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

b)

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

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