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Y < 2x – 3y > -6x + 9

User E Player
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Given the inequality equations

y < 2x – 3 ....... 1

y > -6x + 9 .........2

We are to find the range of interval of x

Rerrange

y-2x< -3

y+6x > 9

From equation 1, make x = 0 and find y

y < 2(0) - 3

y< 0-3

y < -3

Also make y = 0 and get x

0 < 2x-3

-2x<-3

Multiply through by -1

x>3

Graph the function of y < -3 and x>3

From equation 2, make x = 0 and find y

y > -6(0) + 9

y> 0+9

y > 9

Also make y = 0 and get x

0 > -6x+9

6x>9

Divide through by 3

2x>3

Divide through by 2

x>3/2

Also graph the function of y > 9 and x>3/2

This is for the first inequality. Upper part will be shaded because if you plug x = 0 and y = 0 into the inequality, it will become

0<2(0)-3

0<-3

Y < 2x – 3y > -6x + 9-example-1
Y < 2x – 3y > -6x + 9-example-2
User Ivan Klass
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