The equation is .

Apply multiplication property of equality: If a = b, then ac = bc.

                 (Multiply each side by 4)

                                (Cancel common terms)

                      (Subtract 7 from each side)

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

                                (Apply addititve inverse property: )

Apply addition property of equality: If a = b, then a + c = b + c.

                (Add to each side)

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

                               (Apply addititve inverse property: )

                         (Least common denominator of 1 and 2 is 2)

                               (Multiply: )

                                     (Add: 6g + g = 7g)

Apply multiplication property of equality: If a = b, then ac = bc.

                             (Multiply each side by 2)

                                   (Cancel common terms)

Apply division property of equality: If a = b, then .

                               (Divide each side by 7)

                                         (Cancel common terms)

Check:

To check the solution, substitute in .

                     (Product of two different signs is negative)

                              (Product of two same signs is positive)

                                   (Subtract: )

                                        (Divide: )

So, the equation is true.

The solution of .