The inequality is .

Apply multiplication property of inequality: Multiply each side by 6.

           (Cancel common terms)

     (Apply distributive property: (b + c)a = ba + ca)

            (Multiply: )

Apply addition property of inequality: Add 4 to each side.

      (Apply additive inverse property: )

            (Apply additive identity property: )

                  (Add: 12 + 4 = 16)

Apply addition property of inequality: Add 30x to each side.

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

               (Apply additive inverse property: )

                    (Apply additive identity property: )

                             (Add: 2x + 30x = 32x)

Apply division property of inequality: Divide each side by 32.

                               (Cancel common terms)

                                (Divide: )

Check:

To check, substitute three different values for x into the original inequality: 0.5, a number less than 0.5, and greater than 0.5.

Let three values are .

If then (This is false)

If then (This is true)

If then (This is true).

The inequality solution set is  .