What is an Equation?

An equation is a statement that shows 2 sides of equal equations and are divided by an equals sign. The purpose of these questions is you want to use legal sequences (which is when you add, subtract, divide, or multiply from both sides equally) and you deduct down to where the variable is isolated and one side has the variable and the other has just the numbers.

What are equivalent equations?

Equivalent equations are algebraic equations that has numbers and letters for the variable. When you solve equivalent equations you have to do the exact same thing to both sides until you have isolated the variable. When you solve an equivalent equation every legal move that you do is equivalent to the last one because the only difference between the 2 is adding or subtracting the same number. It can be put back to the original equation using only legal moves

How to solve equations?

What you do to solve the equations is remember that they are split in 2 by the equals sign and then you do legal equations equally to both sides. For example if you added 6 to one side then you would also have to do it to the other side. The whole goal is to this until you have isolated the variable and then you can figure it out using math we have previously learned. Lets say that the question is 4x + 7 = 2x + 12. The first move I would do would be remove 2x and get a zero pair. That would leave me with 2x + 7 = 12, This equation is equivalent with the starting equation because i used legal moves to get to this point. Next up I would remove 7 and then what i am left with is 2x = 5. simplifying it down to x = 2.5 is still an equivalent equation to starting equation.

How to verify.

verifying the number is very similar to how you solve it. You put the number you came up with as your answer in the spot that was the variable before. Then you do the exact same legal addition or subtraction until you get back to the same question you started with. If you cant get to the question you started with using only legal moves you did it wrong but if it the same you have done it right

Vocabulary

Equation- an equation is when there are 2 different sets of numbers and they are divided by an equal sign.

Equivalent- Equivalent means that the 2 things are the same. Equivalent equations which is what we are doing can appear different but if you added for example 4 to each side they would still be equivalent equations because it can be reversed with legal moves.

Solution- A solution is the answer to the question. An example would be 3x = 9 the solution would be 3.

Coefficient- a coefficient is the number before the variable displayed. It lets the person know how many of the variable there are.

Zero pairs- zero pairs are made when you add a legal move to the equation and it makes it zero. An example would be 4x + 2 = 11 how you would make a zero pair by subtracting 2 on both sides. it would become a zero pair because you subtract 2 from a positive 2 leaving you with zero. That would leave it as 4x = 9. Zero pairs are crucial for finding the answers to linear equations.

Variable- a variable is what the x is in linear equations. it can be done with any letter but it is representing the unknown. The whole point of the linear equations questions is to solve how much 1 of the variable is worth.

Constant- The constant is a number in the equation that does not have a variable attached. Constants are worth whatever they say they are even when the answer is completed.

Common Denominator- The common denominator is when you have 2 fractions that have the same denominator. It is important because it makes it so you can easily add subtract or divide fractions.  The way you can make a common denominator when they are different is you have to find the lowest common multiple. Lets say your denominators are a 6 and a 7. The lowest common denominator is 42. Then what you do is multiply the numerator by the amount of times you multiplied the denominator and then they are equal.

Distribute- distributing is when there is a number in front of a bracket so you multiply each thing in the bracket by the number outside of the bracket separately and then the number on the outside disappears.