What I learned about grade 9 solving equationsWhat I learned about grade 9 solving equations

• What is an equation?

An equation is an expression that is equal on both sides. For example  : 5+4=3=6

• What are equivalent equations?

Equivalent equations are expressions that are equal to each other. For example: 3x-5=16 ; 3x=21; x=7

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

To solve an equation you need to follow a couple of simple rules and you will end up with the right answer. Whatever you do to one side you have to do to both sides of the equation, you can add like terms, use the distributive rule.  You want to end up with x on one side of the equation and the number on the other.

Ex.

4x+9 = 3x-3

-3x      = -3x

x+9     = -3

-9     = -9

x = -9

• Visually with algebra tiles

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I didn’t put it in there but after you would divide it on btoh sides, so X=1

1.  Algabraically

   3x+9 = 5x-2

   -3x      = -3x

   9     = 2x-2

   +2    =      +2

   2x=11

   2/11 = 2x/2

x= 5 1/2

• BFSD (brackets, fractions, sort, divide)

If you get a messy equation you have to clean up before you start and it makes it a lot easier on yourself. If there is a bracket you have to distribute, if you have fractions you have to take the lowest common denominator and divide the bottom by it and then multiply the top number by it and you get rid of all the fractions. For sorting you can combine like terms to make things faster. You have to divide it in the end.

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

To check your answers you replace all the x’s in the equation with the number or fraction you got and if you did it right both sides will equal the same thing.

• Vocabulary:  equation, equivalent, solution, coefficient, zero pairs, variable, constant, common denominator, distribute

• Equation:   A expression with two things are equal. It has two expressions, one on each side of an equal sign.
• Equivalent: Both sides are equal
• Solution: the solution set is the set containing values of the variables that work for all equations.
• Coefficient: The coefficient is the number with the variable. For ex:  6x; coefficient is 6.
• Zero pair: A zero pair is when you add or subtract something and it’s the same number it makes a zero pair. For ex: 6+ -6 =0; so sense it’s even positive and negative it equals 0 and they cancel out.
• Variable: The variable is the number attached to the number, but it doesn’t have to have a number attached. For ex. 5x; x is the variable.
• Constant: It is the last number by itself without a variable. For ex: 5x+9=9y+4; 9 and 4 are the constants.
• Common: A group of numbers that can be multiplied to equal a number. For ex: 1,2,3,4,6,12
• Distribute: Distributing is when there is a bracket and you take the number in front and multiply all the numbers in the bracket by it and you get rid of the brackets. For ex: 3(2+3) = 6+9