\"\"\"\"\"\"

\

The equation is \"\".

\

Apply division property of equality: Divide each side by 3.

\

\"\"

\

\"\"                       (Cancel common terms)

\

Write two cases:

\

Case-1: a = b

\

\"\"

\

Case-2: a = \"\"b

\

\"\"\"\"

\

Solve the equation for Case-2.

\

Apply multiplication property of equality: Multiply each side by 3.

\

\"\"

\

\"\"                     (Cancel common terms)

\

Distribute terms using distributive property: a(b \"\" c) = ab \"\" ac.

\

\"\"

\

\"\"                      (Multiply: \"\")\"\"

\

Apply addition property of equality: Add 15 to each side.

\

\"\"

\

\"\"                      (Apply Additive inverse property: \"\")

\

\"\"     (Subtract 2p from each side)

\

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

\

\"\"

\

\"\"                      (Apply Additive inverse property: \"\")

\

\"\"                                (Subtract: \"\")\"\"

\

Check:

\

To check the solution, substitute \"\" in original equation.

\

\"\"

\

\"\"                 (Subtract: \"\")

\

\"\"                (Absolute value of |10| is 10)

\

30 = 30                           (Multiply: \"\")

\

Compare the values the equation is true. \"\" is a solution.

\

\"\"

\

Solve the equation for Case-2.

\

Apply multiplication property of equality: Multiply each side by 3.

\

\"\"

\

\"\"                      (Cancel common terms)

\

Distribute terms using distributive property: a(b \"\" c) = ab \"\" ac.

\

\"\"

\

\"\"                       (Multiply: \"\")\"\"

\

Apply addition property of equality: Add 15 to each side.

\

\"\"

\

\"\"                     (Apply Additive inverse property: \"\")

\

\"\"    (Add 2p to each side)

\

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

\

\"\"

\

\"\"                         (Apply Additive inverse property: \"\")

\

\"\"                                  (Add: \"\")\"\"

\

Apply division property of equality: Divide each side by 5.

\

\"\"

\

\"\"                              (Cancel common terms)

\

\"\"                                   (Divide: \"\")\"\"

\

Check:

\

To check the solution, substitute \"\" in original equation.

\

\"\"

\

\"\"                     (Subtract : \"\")

\

\"\"                       (Absolute value of |\"\"2| is 2)

\

6 = 6                                   (Multiply: \"\")

\

Compare the values the equation is true. \"\" is a solution.

\

\"\"

\

The solutions are 15 and 3.

\

The solution set is \"\".