Answer:
Number lines Inequality
First ⇔ [tex]\dfrac{x}{4}\leq\dfrac{-3}{2}[/tex]
Second ⇔ [tex]\dfrac{-75x}{4}>\dfrac{225}{2}[/tex]
Third ⇔ [tex]\dfrac{2x}{3}>\dfrac{-16}{3}[/tex]
Fourth ⇔ [tex]\dfrac{7x}{9}>\dfrac{-14}{3}[/tex]
Step-by-step explanation:
Inequality 1. [tex]\dfrac{7x}{9}>\dfrac{-14}{3}[/tex]
Multiply both sides by 9 , we get
[tex]7x>-42[/tex]
Divide both sides by 7, we get
[tex]x>-6[/tex] which is shown by the fourth number line.
Inequality 2. [tex]\dfrac{-75x}{4}>\dfrac{225}{2}[/tex]
Multiply both sides by 4 , we get
[tex]-75x>450[/tex]
Divide both sides by -6, we get
[tex]x<-6[/tex] which is shown by the second number line.
Inequality 3. [tex]\dfrac{x}{4}\leq\dfrac{-3}{2}[/tex]
Multiply both sides by 4 , we get
[tex]x\leq-6[/tex] which is shown by the first number line.
Inequality 2. [tex]\dfrac{2x}{3}>\dfrac{-16}{3}[/tex]
Multiply both sides by 3 , we get
[tex]2x>-16[/tex]
Divide both sides by 2, we get
[tex]x>8[/tex] which is shown by the third number line.
