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Grade 9/Math/MPM1DZ/Unit 3: Solving Equations and Inequalities.md

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+# Unit 3: Solving Equations and Inequailties
+
+## Equations
+- a ```mathematical statement``` in which the value on the ```left side``` equals the value on the ```right side``` of the equal sign     
+- To ```solve``` and equation is to find the variable that makes the statement true
+### Methods to solve an equation
+ 1. Expand and simplify both sides
+ 2. Isolate using reverse order of operations
+ 3. Check the solution by plugging the variable back into the equation and check if the ```left side``` equals the ```right side```
+   
+## Absolute Values 
+- There are 2 cases. For this sort of equation, you must split the equation into 2 separate equations. One of the
+- equations will have the absolute bracket be positive while the other negative.   
+- Absolute values are written in the form $`| x |`$
+- where    
+$`
+| x | =
+\begin{cases}
+x, & \text{if  } x > 0\\
+0, & \text{if  } x = 0\\
+-x, & \text{if  } x < 0
+\end{cases}
+`$
+
+## Quadractic Equations
+- ```Quadratic Function```: A parabolic graph where the axis of symmetry is parallel to the y-axis    
+- ```Quadratic Equation```: This function is set equal to ```0```. The solution to the equation are called ```roots```     
+- Solve quadratic equation by:    
+
+  1. Isolation    
+     - $`a(x+b)^2 + k = 0`$
+  2. Factor using zero-product property    
+     - ```The Zero Factor Property``` refers to when a&times;b=0, then either a=0 or b=0.     
+     - $`(x-a)(x-b)=0`$    
+     - $`x = a, b`$      
+
+- <img src="http://www.assignmentpoint.com/wp-content/uploads/2017/12/Quadratic-Expression-1.jpg" width="400">
+
+**Note:**   
+- &radic;x<sup>2</sup> = &plusmn; x (There are 2 possible solutions)
+- ```Distrubutive Property``` - This is opening the bracket. a(x+y) = ax+ay    
+    
+## Tips
+- ```Absolute Values``` can have 2 solutions     
+- ```Quadratics``` can also have 2 solutions    
+- Make sure to do the reverse when moving things to the other side, meaning a positive on the ```left side``` becomes a negative on the ```right side```