What is an equation?
An equation is a mathematic statement showing that on both sides of the equal sign that the two statements are equal to each other.
What are equivalent equations?
Equivalent equations are two or more algebraic equations that have the same solution as each other.
How to solve equations (find what x = ?)
Visually with algebra tiles:
First, model the equation with the tiles. After that, to find x, you need to make legal moves. Using legal moves helps you isolate the variable to help you find the solution. A legal move is doing the same move on both sides of the equation. A move you can do is adding tiles or taking away tiles. With legal moves, you need to create zero pairs. A zero pair is when you make a legal move to make one term to cancel itself out. But, if one term cancels itself out, its like term will get the same move that its like term got. Eventually, you will get to the point where you cannot do anymore moves because you have the smallest possible set of x’s on one side and the “ones” on the other. The final step is to divide. You have to divide the amount of x’s by the amount of ones.
Algebraically:
An easy way to solve an algebraic equation on paper is to visualize the equation in your mind with algebra tiles. Creating zero pairs with legal moves is your next step. A good way to keep track and to show your work with zero pairs is to cross out the zero pair with a large letter “z”. Keep making legal moves until you get to your final divide step.
BFSD (brackets, fractions, sort, divide)
This acronym is pretty self explanatory. It is a lot like BEDMAS or PEMDAS. In an equation, you might counter brackets or fractions. The first thing to do is distribute. This is the exact same distributing as any other equation. With the fractions, you need to find the lowest common denominator and multiply everything in the equation by the LCD. With the fractions being multiplied, you need to simplify by changing the fraction to a whole number. The next two steps are easy and self explanatory.
How to verify (Check) a solution (answer) is correct
After you have came to a conclusion on your answer, with every x in the equation, you replace it with your answer.
Vocabulary (Definitions):
Equation: a statement that the values of two mathematical expressions are equal (indicated by the sign =).
Equivalent: equal in value, amount, function, meaning, etc.
Solution: a means of solving a problem or dealing with a difficult situation.
Coefficient: a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
Zero pairs: a pair of numbers whose sum is zero, e.g. +1, -1. • used to illustrate addition and subtraction problems. with positive and negative integers.
Variable: A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable
Constant: A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
Common denominator: a shared multiple of the denominators of several fractions.
Distribute: Distributing items is an act of spreading them out equally. Algebraic distribution means to multiply each of the terms within the parentheses by another term that is outside the parentheses.