What is an equation?
A statement that the values of two mathematical expressions are equal. An equation has numbers and variables on both sides of the equal sign. For example -5+3x = 4x+3. To make one side equal the other you need to use legal moves. A legal move is when you do one thing to one side you do it to the other. There are many legal moves that you can use. You can add things to both sides, subtract things from both sides, multiply things on both sides, divide things on both sides, and take away things from both sides. When trying to solve an equation with variables you are trying to isolate the variable and find out the value of the variable. For example if you have -8+4x = 5x-6 you want to try and figure out what the value of x is. When solving an equation you want to try and make zero pairs. A zero pair is when there are 2 opposite numbers on the same side of the equal sign. For example if you have -8+3x+8 = 4x.
What are equivalent equations?
Equivalent equations are algebraic equations that have identical solutions. You can make an equivalent equation by adding the same thing to both sides. For example if you have 3+4x = 2-5x. If you add +4 to both sides you will get 7+4x = 6-5x which is equivalent to 3+4x = 2-5x. Another way you can make an equivalent equation is by subtracting the same thing from both sides. For example if you have -5+3x = +3 and you subtract 2 from both sides you get -7+3x = -1 which is equivalent to -5+3x = +3. Another way to make an equivalent equation is by multiplying the same thing to both sides. For example if you have 3x-4 = 5x-6 and you multiply both sides by +6 you get 18x-24 = 30x-36 is equivalent to 3x-4 = 5x-6. A final way to make an equivalent equation is by dividing both sides. For example if you have -9x+3 = 6x and you divide both sides by +3 you get -3x+1 = 2x which is equivalent -9x+3 = 6x.
How to solve equations (find what x = ?)
Visually with algebra tiles
Algebraically
BFSD (brackets, fractions, sort, divide)
BFSD is the order that you solve an equation with numbers and variables. The B stands for brackets. The first step when solving an equation is to remove brackets. To do this you might distribute or combine like terms. The F stands for fractions. The second step when solving an equation is to get rid of the fractions. To do this you multiply all the numbers and the fractions numerators by the LCD of all the fractions. Then you divide the numerator by the denominator to get a whole number. The S stands for sort. The third step when solving an equation is to sort. To sort you have to do legal moves until you have the variable on one side and the whole numbers on the other. For example 9x = 36. The D stands for divide. The last and final step when solving an equation is to divide. You divide both sides by the number that has the variable next to it. For example if you have 6x = 42 you would divide both sides by +6.
How to verify (Check) a solution (answer) is correct?
Once you have your answer you are going to want to check and see if it’s right. How you check if your answer is right is by taking your answer and putting that number where all the variables are. For example if you have 2x+3 = 15 and you solved x = 6, then you would insert 6 where all the x’s are. 2(6)+3 = 15. 2 times 6 equals 12, and 12+3= 15. 15 = 15. Both sides equal the same so you know the value of x is 6.
Vocabulary:
Equation – A statement that the values of two mathematical expressions are equal
Equivalent – Equal in value. An equivalent equation is an equation that has identical solutions
Solution – A value that makes the equation true
Coefficient – A coefficient is the number in front of the variable. If there is no number the coefficient is one
Zero pairs – A pair of numbers whose sum is zero, e.g. +1, -1.
Variable – Is a symbol or letter, such as “x” or “y,” that represents a value
Constant – The constant is a number in an equation that stays the same no matter what value the variable is. If there is no constant the constant is zero
Common Denominator – Is a number which can be divided exactly by all the denominators in a group of fractions
Distribute – Gives or shares something; deal out