Reflections should be completed after you present.
Your reflection must answer every question below using full sentences. Your reflection should be between ⅓ of a page and 1 page long.
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Variables on Both Sides
Below is a great video found by a group that presented on multi-step equations.
Combining Like Terms
Solve equations with more than one like term the same way that you simplified expressions with more than one like term.
x + 3 + 4 + 5x - 6 + (-8x) = 1 + -9 Look for all the terms that are the same and pay attention to the sign in front of each one. x + 5x + -8x can go together to make -2x 3 + 4 - 6 can go together to make 1 1 + -9 can go together to make -8. Notice that you can't combine terms that are on opposite sides of the equation because the equal sign is separating those terms. You can only combine those terms by using the inverse operation. We simplified the equation to look like -2x + 1 = -8 Following the order of operations, we would multiply 2 and x together first, then subtract 1, so to solve the equation we work backwards using the inverse operation for each step. This means we will add 1 first, then divide x by 2. -2x + 1 = -8 -1 -1 -2x = -9 /-2 /-2 x = 4.5 or 4 1/2 Distributive Property
A video from a student explains this concept perfectly.
Fractions
This type of equation can be confusing if you don't understand that we are working with the order of operations (PEMDAS) in reverse. This means that whatever you would do first when you simplify the expression would now come last as its inverse. Below are a couple examples and a very helpful video.
Notes: An equation is a problem that uses an equal sign to show that both sides of the equation are balanced. In a 2-step equation, you have exactly 2 operations that are affecting the variable. In order to solve a 2-step equation, you must undo these 2 things by doing the inverse operation in order to isolate the variable, or get it by itself, to one side of the equation. When you undo the operations on one side, you must do the same thing on the other side so the equation stays balanced. With two-step equations, you have to undo addition or subtraction first, then undo multiplication or division because you are working backwards with the order of operations. Practice: This powerpoint explains 2-step equations step by step and includes several practice problems. ***Working with -x *** If the variable is negative with no number beside it, it means that the variable has been multiplied by a -1. Remember that we don't write 1 beside the variable because it is understood that x is the same as 1x. The same thing is true for -x and -1x. To solve an equation with a negative variable, undo addition or subtraction first, then undo the negative coefficient by dividing by the negative. These are the same steps as usual. Example: -x + 6 = -10 -6 -6 -x = -16 /-1 /-1 x = 16
Essential Question: Why do we use inverse operations when solving an equation? Provide the inverse of each operation. Notes: A 1-step equation is an equation that involves one operation. In order to solve the equation, you must use the inverse operation, or do the opposite of the operation in the equation. For example, the inverse of addition is subtraction. When you undo the operations by using the inverse, you will isolate the variable to get it by itself on one side of the equation. When you perform the inverse operation on one side of the equation, you must do it to the other side so both sides remain balanced and equal. Solving 1-step equations video More notes below. Practice: Jeopardy
Essential Questions:
What can an equation be compared to? What is an equation made up of? In the real world, when might you use an equation? Come up with an example to justify your answer. Notes: This site compares and contrasts expressions and equations. |
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