Question

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

Match each inequality to the number line that represents its solution
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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:

`(7x)/(9)>-(14)/(3)\\\\x>-(14)/(3)*(9)/(7)>-(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:

`-(75x)/(4)>(225)/(2)\\\\(75x)/(4)<-(225)/(2)\\\\x<-(225)/(2)*(4)/(75)<-6`

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

- Third inequality:

`(x)/(4)\leq -(3)/(2)\\\\x\leq -(3)/(2)*4\leq -(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:

`(2x)/(3)>-(16)/(3)\\\\x>-(16)/(3)*(3)/(2)>-(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!