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Daily Quiz -
Simplify the expression, then create your own realistic scenario for the final expression.
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2(x − 2(1 − x))
Simplify Expression Check
Complete in your notes as Practice!1.
2.
3. Multiply the quantity by (-5) and add the product to the quantity
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−4(x 2 − 2x) + 2x(3 +1)
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6 x −1
2(x −1)
⎡ ⎣ ⎢
⎤ ⎦ ⎥
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2x 2 − 8xy + 5y 3
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7x 2 − 8xy + 3y 2
Objectives:
SWBAT… Create and carry out a plan for solving
equations Maintain equality when solving
equations through inverse operations and simplification techniques (such as combining like terms)
Solve one-step linear equations Solve multi-step linear equations
● A variable is a letter which represents an unknown number. Any letter can be used as a variable.
● An algebraic expression contains at least one variable.
Examples: a, x+5, 3y – 2z
● A verbal expression uses words to translate algebraic expressions.
Example:“The sum of a number and 3” represents “n+3.”
● An equation is a sentence that states that two mathematical expressions are equal.
● Linear Equation in One Variable - can be written in the form ax +b =c, a 0
Example: 2x-16=18
Review of Key Concepts
Key Concepts Continued● To solve means to find the value of a variable ● Inverse Operations are operations that “undo”
each other ● division and multiplication● addition and subtraction
● Isolate a Variable is part of the process of solving, in which the variable is placed on one side of the equation by itself
● Equality is the state of being equal or having the same value – we always maintain equality when solving equations
● A solution is a value that can take the place of a variable to make an equation true
Solving equations is just a matter of undoing operations that are being done to the
variable.In a simple equation, this may mean that we only have to undo one operation, as in the
following example.Solve the following equation for x
x + 3 = 8
x + 3 = 8 the variable is x
x + 3 – 3 = 8 – 3 we are adding 3 to the variable, so
to get rid of the added 3, we do the opposite--- subtract 3.
x = 5 remember to do this to both sides of the equation.
Single-Step Linear Equation
In an equation which has more than one operation, we have to undo the operations in the correct order.
Solve the following equation: 5x – 2 =13 5x – 2 = 13 The variable is x
5x – 2 + 2 = 13 + 2 We are multiplying it by 5, and subtracting 2
First, undo the subtracting by adding 2.
5x = 15 Then, undo the multiplication by dividing by 5.
5 5 x = 3
Multi-Step Linear Equation
We start with the operation the farthest away from the variable!
Steps to Solving Equations● Simplify each side of the equation, if needed, by
distributing or combining like terms.● Move variables to one side of the equation by
using the opposite operation of addition or subtraction.
● Isolate the variable by applying the opposite operation to each side.
• First, use the opposite operation of addition or subtraction.
• Second, use the opposite operation of multiplication or division.
● Check your answer.
How can we “undo” operations? Isn’t this wrong?
Addition Property of Equality – states you can add the same amount to both sides of an equation
and the equation remains true.2 + 3 = 5
2 + 3 + 4 = 5 + 4 9 = 9 ? true
Subtraction Property of Equality – states you can subtract the same amount from both sides of an
equation and the equation remains true.4 + 7 = 11
4 + 7 – 3 = 11 – 3 8 = 8 ? true
Example
5(3 + z) – (8z + 9) = – 4z
15 + 5z – 8z – 9 = – 4z (Use distributive property)
6 – 3z = – 4z (Simplify left side)
6 + z = 0 (Simplify both sides)
z = – 6 (Simplify both sides)
6 – 3z + 4z = – 4z + 4z (Add 4z to both sides)
6 + (– 6) + z = 0 +( – 6) (Add –6 to both sides)
Multiplication Property of Equality – states you can multiply the same amount on both sides of an equation and the equation remains true.
4 · 3 = 122 · 4 · 3 = 12 · 2
24 = 24Division Property of Equality – states you can divide the same amount on both sides of an equation and the equation remains true.
4 · 3 = 124 · 3 = 12
2 212 = 6
2
Example
– y = 8
y = – 8 (Simplify both sides)
(– 1)(– y) = 8(– 1) (Multiply both sides by –1)
Example
Recall that multiplying by a number is equivalent to dividing by its reciprocal
3z – 1 = 26
3z = 27 (Simplify both sides)
z = 9 (Simplify both sides)
3z – 1 + 1 = 26 + 1 (Add 1 to both sides)
(Divide both sides by 3)3
27
3
3
z
Special Cases
No Solution – we arrive at an answer that does not maintain equality
Infinite – we arrive at an answer that will always maintain equality (always be true)
Partner Practice in Notes