What is an equation?  

An equation is where there are numbers, terms and variables with an equal sign and a number on the other side of the equal sign. An equation is where the left side of the equal sign is equal to the right side. Equations are like expressions, where in expressions there are different terms, but in an equation, there is an equal sign, stating that the two sided are equal. 

What are equivalent equations?   

Equivalent equations are when multiple equations all equal to the same variable. It is when there is an equation each have different terms and numbers in then, but the variable is the same in everyone. 

How to solve equations (find what x =?): 

• Algebraically 

There are many different steps that you need to do to solve equations, but there are only certain moves that you can do called legal moves. One of the legal moves that you can do is take away zero pairs that are opposite of each other (if there is 2x and –2x you can take them all away as long as they are on the same side). Another legal move is adding or taking away. The goal when solving equations is trying to get x on one side and the numbers on the other side. If there is an equation where there is (3x + 4) on one side and (–2x + 3) on the other side, you could add 2x to each side so one of the sides make zero pairs and all of the x’s are on one side. There are some equations that contain fractions and decimals and those are hard to solve if you leave it in that form. To make it easier to solve with fractions there are two things that you could do. The first thing that you can do is find a common denominator between the other fractions that are in the equation, but if there is only one fraction you can make the other numbers into fractions. Another way that you can change the fractions is you can multiply all of the denominators together and then you have to multiply each term by that number. Once you have multiplied the terms you divide the numerator by the denominator. If there is a decimal in the equation, they you can multiply it depending on the decimal placement (x10, x100, etc.). 

• Visually with algebra tiles  

To solve equations in a visual way you can use algebra tiles. Algebra tiles are used to display the equation in an easy to solve way. When using the algebra tiles, you would have a line down the middle to act as the equal sign, the long skinny blocks to show x, the small squares to show 1, the dark side is positive and the light side would be negative. It is a lot easier to take things out and add them in and once you find x it is also easy to divide the number equally. 

• BFSD (brackets, fractions, sort, divide)  

When you are solving equations, you cannot just solve them across, you have to follow steps. The first thing you do is the brackets. When working with any equation you always want to get rid of the brackets first, and to do that you have to distribute whatever is on the outside on the bracket to everything that is on the inside of it. Once you have gotten rid of your brackets you want to get rid of the fractions. To get rid of your fractions you multiply the denominators to find a common denominator. After you want to sort, which means that you can combine the like terms to simplify and you can get rid of any zero pairs. 

 

How to verify (Check) a solution (answer) is correct: 

Once you are finished solving your equation it is always good to double check your answer because there is only one possible answer. To double check your answer to your equation you take your answer and switch it with the variable and then solve the equations algebraically. 

Vocabulary: 

Equation – An equation is when there are two mathematical expressions that are equal to each other and they are indicated by an equal sign. 

Equivalent – Equivalent means that they are equal in value. 

Solution – The solution in an equation is the answer. 

Coefficient – A coefficient is a number that is in front of a variable. 

Zero pairs – A zero pair is when there is a negative and a positive of the same kind, that cancel each other out. 

Variable – The variable is what you are solving for, the unknown value. 

Constant – The constant is the number that is by itself with no variable. 

Common denominator – A common denominator is a common multiple that is found within the denominators of several fractions. 

Distribute – Distributing means to multiply each of the terms within the brackets by the term that is outside of the brackets.