Check Your Skills Answer Key

1. Must Be True

   Because v is already greater than t, adding a negative number to t will only make it smaller.

2. Must Be True

   One way to prove this statement is always true is to add inequalities. You know that v > t, and that s > r. Thus:

   
3. Not Always True

   Point v could be any positive number, and r and s could be any negative number.

   If r = −3, s = −2, and v = 4, then rs > v.

   If, however, r = −2, s = −1/2, and v = 3, v > rs.

4. 

   To find x, you need to figure out how far apart tick marks are. You can use the two given points () to do so. There are five intervals between the two points. Thus:

   

   If the distance between tick marks is , then x is: .

5. 6

   Start with the points X, Y, and Z. There are two possible arrangements:

   

   Now place U on each number line:

   

   On one number line, , but the question stated that , so must equal 6.