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