Answer with explanation:
1)
[tex]\dfrac{7x}{9}>\dfrac{-14}{3}[/tex]
On solving we get:
[tex]x>-6[/tex]
Hence, the shaded region is to the right of -6 with open circle at -6.
2)
[tex]\dfrac{-75x}{4}>\dfrac{225}{2}[/tex]
On solving we get:
[tex]-x>\dfrac{225}{2}\times \dfrac{4}{75}\\\\\\-x>6[/tex]
on multiplying both side of the inequality by -1 we get:
[tex]x<-6[/tex]
Hence, the shaded region will be to the left of -6 and open circle at -6.
( Since, the inequality is strict)
3)
[tex]\dfrac{x}{4}\leq \dfrac{-3}{2}\\\\\\x\leq \dfrac{-3}{2}\times 4\\\\\\x\leq -6[/tex]
The graph of this will be shaded region to the left of -6 and closed circle at -6.
Since the inequality is an inequality with a equality sign.
4)
[tex]\dfrac{2x}{3}>\dfrac{-16}{3}\\\\\\x>\dfrac{-16}{3}\times \dfrac{3}{2}\\\\\\x>-8[/tex]
Hence, the graph is a number line with shaded region to the right of -8 and open circle at -8.
( Since, the inequality is strict )
