Daily Quiz - Simplify the expression, then create your own realistic scenario for the final...

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