The inequality is .

Apply subtraction property of inequality: Subtract 1.5 from each side.

    (Apply additive inverse property: )

          (Apply additive identity property: )

                   (Subtract: )

Apply subtraction property of inequality: Subtract 2.5z from each side.

Apply commutative property of addition: a + b = b + a.

         (Apply additive inverse property: )

               (Apply additive identity property: )

                          (Subtract: )

Apply division property of inequality: Divide each side by 3.1.

                              (Cancel common terms)

                                   (Divide: )

Check:

To check, substitute three different values for z into the original inequality: , a number less than , and greater than .

Let three values are .

If then (This is true)

If then (This is false)

If then (This is false).

The inequality solution set is  .