Directions: Write an inequality whose solution set is x < -1/2 by filling in the boxes with whole numbers 0 through 9, using each number at most once.

### Hint

### Hint

What does it mean to have a solution set in an inequality? How can you use the solution set “border number” to help you write an inequality?

### Answer

### Answer

There are many correct answers. Some possible responses could be:

2x + 5 > 4x + 6;

1x + 5 > 7x + 8;

9x + 6 < 5x + 4

2x + 5 > 4x + 6;

1x + 5 > 7x + 8;

9x + 6 < 5x + 4

Source: Daniel Luevanos

I love this question. I’ve been wondering what to call the “border number.” I’ve been calling it a “limit.” What are your thoughts on that?

Glad you like the question, Lane! I usually refer to the “border number” or “limit” as the “boundary point.” I never thought about using “limit” as part of my discussion with students, but now I’m going to. Thanks!

My students also came up with these solutions:

1x + 4 > 3x + 5

1x + 5 > 3x + 6

1x + 7 > 3x + 8

1x + 8 > 3x + 9

5x + 8 > 7x + 9

2x + 5 > 4x + 6

4x + 8 > 6x + 9

These are all great solutions! Thank you for sharing!