Directions: Using the digits 1 to 9, at most one time each, make a compound inequality that has the largest interval.

### Hint

How does changing the coefficient affect the resulting value?

How does changing the constant next to x affect the resulting value?

How does changing the constant next to x affect the resulting value?

### Answer

The largest possible interval is just less than 7 units long. You can get that from inequalities like:

2 ≤ 1x + # < 9

# can be any of the remaining numbers as it acts like a translation and doesn’t affect the size of the interval.

Source: Robert Kaplinsky