Question

Frank cut a 52 inch string into 3 pieces. The first piece is 20 inches long. The second piece is at least 12 inches long, but no greater than 18 inches long. Which inequality represents the length (x) of the third piece?

Answer 1

We need to figure out how much string would be left, after taking away the first two pieces.
We know that the first piece is 20 inches long, so we can say that there is 52-20 inches left, or 32 inches.

The second piece is between 12 and 18 inches, meaning that there would be between 32-12 and 32-18 inches left for the third piece, or 20 and 14 inches. This means that the third piece would be at least 14 inches long, but no more than 20, since we don’t have more string than that (20+12+20=52, and 20+14+18=52)

So we can say that x is greater or equal to 14, but less than or equal to 20, or:

14<=x<=20 (“<=“ is written like a normal “<“ sign with a line _ right under it)