Question

Drag the tiles to the correct boxes to complete the pairs.

Answer 1

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:

$\frac{7x}{9}>-\frac{14}{3}\\\\x>-\frac{14}{3}*\frac{9}{7}>-\frac{126}{21}>-6 \\\\x>-6$

Therefore, the solution for the first inequality is the x greaters than 6, and the solution matchs with the fourth number line.

- Second inequality:

$-\frac{75x}{4}>\frac{225}{2}\\\\\frac{75x}{4}$

Therefore, the solution for the first inequality is the x less than 6, and the solution matchs with the second number line.

- Third inequality:

$\frac{x}{4}\leq -\frac{3}{2}\\\\x\leq -\frac{3}{2}*4\leq -\frac{12}{2}=-6$

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:

$\frac{2x}{3}>-\frac{16}{3}\\\\x>-\frac{16}{3}*\frac{3}{2}>-\frac{48}{6}>-8\\\\x>-8$

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!