Question

Which ordered pair is a solution to the inequality?

Answer 1

`\large\boxed{\left(-3,\ -(1)/(2)\right)}`

Explanation:

Convert the inequality to the form y > mx + b:

`-(2)/(3)x-4y>0` add 2/3x to both sides

`-4y>(2)/(3)x` change the signs

`4y<-(2)/(3)x` divide both sides by 4

`y<-(2)/((3)(4))x`

`y<-(1)/(6)x`

Put the coordinates of the points to the inequality and check:

for (-15, 3):

`3<-(1)/(6)(-15)\to3<(5)/(2)\qquad FALSE`

for (6, 3):

`3<-(1)/(6)(6)\to 3<-1\qquad FALSE`

for (-3, -1/2):

`-(1)/(2)<-(1)/(6)(-3)\to-(1)/(2)<(1)/(2)\qquad TRUE`

for (6, -1/4):

`-(1)/(4)<-(1)/(6)(6)\to-(1)/(4)<-1\qquad FALSE`

Answer 2

(-3, -1/2)

Explanation:

Plug in the numbers for x and y. If the left side of the equation is greater than the right side (0), then ordered pair is a solution to the inequality.