Hello!
The answer is:
- First inequality: The fourth number line.
- Second inequality: The second number line.
- Third inequality: The first number line.
- Fourth inequality: The third number line.
Why?
To be able to match each inequality to the number line that represents its solution, we need to solve each inequality.
So, solving we have:
- First inequality:
[tex]\frac{7x}{9}>-\frac{14}{3}\\\\x>-\frac{14}{3}*\frac{9}{7}>-\frac{126}{21}>-6 \\\\x>-6[/tex]
Therefore, the solution for the first inequality is the x greaters than 6, and the solution matchs with the fourth number line.
- Second inequality:
[tex]-\frac{75x}{4}>\frac{225}{2}\\\\\frac{75x}{4}<-\frac{225}{2}\\\\x<-\frac{225}{2}*\frac{4}{75}<-6[/tex]
Therefore, the solution for the first inequality is the x less than 6, and the solution matchs with the second number line.
- Third inequality:
[tex]\frac{x}{4}\leq -\frac{3}{2}\\\\x\leq -\frac{3}{2}*4\leq -\frac{12}{2}=-6[/tex]
Therefore, the solution for the first inequality is the x less or equals than 6, and the solution matchs with the first number line.
- Fourth inequality:
[tex]\frac{2x}{3}>-\frac{16}{3}\\\\x>-\frac{16}{3}*\frac{3}{2}>-\frac{48}{6}>-8\\\\x>-8[/tex]
Therefore, the solution for the first inequality is the x greater than 6, and the solution matchs with the third number line.
Have a nice day!
