# Create an Inequality, Given a Solution Set

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create an inequality whose solution set is x < -1/2.

### 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?

There are many correct answers. Some possible responses could be:
2x + 5 > 4x + 6;
1x + 5 > 7x + 8;
9x + 6 < 5x + 4

Source: Daniel Luevanos

## Difference of Squares and Sum of Cubes

Directions: Using the digits 0 to 9 at most one time each, place a digit …

1. 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!

2. 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

3. Thank you very much for the help to develop us students by helping us some difficult questions we can´t manage. May God bless you

4. Thank you very much for the problem!

I have a student that developed an equation to represent the situation as long as no number is repeated, where x is any number between 1 and 9.

x + (constant) > x +1 + (constant + 2)