What is an equation?
An equation is a mathematical statement that contains an equal sign included. An example could be x 
= 5 that may not look like an equation, but you must have that = sign. This image shows 3 different types of equations, it is proven that they all are equations but presented different.
What are equivalent equations ?
Equivalent equations are two equations that have the same value on either side. An equivalent equation is when there are two equations that 
have the same value on either side. An example could be, 3+2x = 21 + 10x those two are an example of equivalent equations. Another example is these 2 on the whiteboard, different types same meaning.
Visually with algebra tiles:
We made our own algebra tiles and using them we solved 
equations. You can also visually draw them; however, that does take more time and not everyone wants to. It is very easy to use the tiles here are the following steps…
Algebraically:
Algebraically is a term used to describe writing the equation in a horizontal matter. You go one step at a time and don’t combine two steps at one’s because you can make mistakes more often. Algebraically doing an equation is a way to write each step on its own like, this way you have less of a chance to make a mistake (get confused) and to miss a step. It is an organized fashion. An example of which, 
BFSD (brackets, fractions, sort, divide):
There are times were equations can be very difficult (ugly). Luckily using BFSD you can simply solve those “ugly” equations. Following the 4 simple steps you will come to an answer easier and possibly faster.
1- Get rid of the brackets
2- Resolve any equations
3- Sort the numbers using legal moves. What is a legal move? It is when you either, add number on both sides of the = sign, subtract numbers from both sides or by creating pairs. Here’s an example:
4- Divide the two numbers remaining.
Following these 4 simple steps you will come to a simple “answer”. These steps come in very handy and personally I try to not forget them and recommend using them.
How to verify (Check) a solution (answer) is correct:
After doing your equation you always want to check if it’s correct. To do so you need to take what x =
and replace x by that answer. Let’s say your equation is….
Once you found out what x is you would use that number replacing x…
However you must pay very close attention to and make sure
you multiply the coefficient by your new number Than you proceed by solving your equation using your commun sense and if both numbers and up the same (example: 2 = 2) than your answer is correct. If the numbers are different, then your original answer is incorrect.
Vocabulary:
Equation: A articulation utilized with numbers and letters and has a break even with sign.
Equivalent: When two numbers or conditions are rise to each other.
Solution: the reply to a condition.
Coefficient: The number some time recently a letter (polynomial math)
Zero pairs: After you include or subtract a number from either side and after that when including or subtracting from that number and the modern number you get is 0, we call that a zero combine.
Variable: Factors are the signs we utilize to include, subtract, duplicate or partition.
Constant: It is the number in a condition that does not have a letter joined to it.
Common denominator: The number that’s some time recently a letter (variable based math)
Distribute: After you have a number before a set of brackets and so to urge freed of the brackets you increase the numbers on the interior of the brackets by the number on the outside of the brackets.