In algebra, there are lots of rules and properties to remember. The good news is that once you understand them, you can apply them in lots of different orders and combinations. Give an example of a mathematic problem that can be solved in multiple ways by applying properties of algebra differently. Explain your reasoning

See below.

Step-by-step explanation:

Step 1 6x + 2 = 6 - 3x    Distributive property of multiplication over addition

Step 2 2 = 6 - 9x    Subtraction property of equality

Step 3 -4 = -9x    Subtraction property of equality

Step 4 4/9 = x    Division property of equality

Step 5 x = 4/9   Symmetric property of equality

Answer & Step-by-step explanation:

Mathematical Problem Example :  100 x 105

By commutative rule, a x b = b x a : 100 x 105 = 105 x 100 = 10500

By distributive rule, a x (b+c) = (a x b)  + (a x c)

Breaking down 105, we get : 100 x 105 = 100 (100 + 5)

= (100 x 100) + (100 x 5) = 10000 + 500 = 10500

As solutions by both rules are same, algebra multiple ways to solve a mathematical problem have been hence proved.