Transcript Simplify both side of equation / inequality

Unit 1:
Evaluating and Simplifying Expressions
Expression: A math statement without an equal sign
(simplify, evaluate, or factor)
Evaluate: Testing a value for a variable in an expression
(using PEMDAS and substitution)
Simplify: To complete all order of operations
(PEMDAS) and properties in an expression
Equation:
A math statement with an equal sign (solve)
Inequality: A math statement with an inequality sign (solve)
Example 1 Evaluating Expressions
Evaluate the following expressions. Let x = 5, y = -2, and z = 2.
a)
2 y 2  11
2
5
z
 3y
c)
4
2
(
3
x
 y)  z
b)
d)
( y  z )2
x y
Example 2 Simplifying Expressions
Simplify the following expressions… Distribute and Combine Like Terms
a)
5x  2x  5 y  3 y
c) 2( x 2  2 x )  ( x 2  x )
b) (5 x  2 y )  (4 x  3 y )  (7 x  8 y )
d)
5( 3m  1)  ( m  7 )
Unit 1: Solving
Linear Equations & Inequalities
[1]
Simplify both side of equation / inequality
[2]
Move the variable to one side.
[3]
Use inverse operations to isolate the variable to equal a
value. Operations must be the same on both sides of
equation. (Inverse Operations order = Backwards of PEMDAS )
Add: +
– :Subtract
Multiply: x, ·
÷ :Divide
Square Root: ...
(...)2 :Square
INEQUALITIES Special Note:
With inequalities if you divide or multiply both sides by a negative
value, switch the inequality sign direction
PRACTICE: Solving Equations
1. 2
3
3.
d 5
34  10w  6w  2
2.
4.
2( 3 x  7)  9  25
5y
2y 
4
6
5.
7.
PRACTICE: Solving Equations
6. 5x – (2x – 2) = 3x – 1
3 y  16  22
6x – (2x + 3) = 2x + 8 8. 5( 2  a )  2  8  3( 2a  1)
Solving Inequalities
When solving inequalities the same rules apply EXCEPT when
you multiply or divide by a negative number…flip the sign!
KEY WORDS:
<
>

≥
Less than
Greater
than
At most
No more
than
At least
No less than
Graphing: Open circle = < , >
Closed circle =  , ≥
1.
x  6  18
2.
2 y  7  11
PRACTICE: Solving Inequalities
4. 15  5t
3.  4( x  1)  21
5.
12  2 x  6 x  12
7.
9z  2  4z  15
6.
8.
 55
x8 x

4
3
5 x  2( x  5)  10  3 x