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

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**Simplify Expression Check**

Complete in your notes as Practice! Multiply the quantity by (-5) and add the product to the quantity

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**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

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Review of Key Concepts 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

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**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

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**Single-Step Linear Equation**

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 = 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 = remember to do this to both sides of the equation.

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**We start with the operation the farthest away from the variable!**

Multi-Step Linear Equation In an equation which has more than one operation, we have to undo the operations in the correct order. We start with the operation the farthest away from the variable! Solve the following equation: 5x – 2 =13 5x – 2 = The variable is x 5x – = We are multiplying it by 5, and subtracting 2 First, undo the subtracting by adding 2. 5x = Then, undo the multiplication by dividing by 5. x = 3

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**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.

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**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 = = = 9 ? true Subtraction Property of Equality – states you can subtract the same amount from both sides of an equation and the equation remains true = – 3 = 11 – = 8 ? true

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Example 5(3 + z) – (8z + 9) = – 4z 15 + 5z – 8z – 9 = – 4z (Use distributive property) 6 – 3z = – 4z (Simplify left side) 6 – 3z + 4z = – 4z + 4z (Add 4z to both sides) 6 + z = (Simplify both sides) 6 + (– 6) + z = 0 +( – 6) (Add –6 to both sides) z = – 6 (Simplify both sides)

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Multiplication Property of Equality – states you can multiply the same amount on both sides of an equation and the equation remains true. 4 · 3 = 12 2 · 4 · 3 = 12 · 2 24 = 24 Division Property of Equality – states you can divide the same amount on both sides of an equation and the equation remains true. 12 = 6 2

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**Example (– 1)(– y) = 8(– 1) (Multiply both sides by –1)**

y = – 8 (Simplify both sides)

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**Example 3z – 1 = 26 3z – 1 + 1 = 26 + 1 (Add 1 to both sides)**

Recall that multiplying by a number is equivalent to dividing by its reciprocal Example 3z – 1 = 26 3z – = (Add 1 to both sides) 3z = 27 (Simplify both sides) (Divide both sides by 3) z = (Simplify both sides)

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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)

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**Partner Practice in Notes**

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Objective - To solve equations over given replacement sets. Equalities Inequalities = Equals- is the same as Congruent- same size and shape Similar- same.

Objective - To solve equations over given replacement sets. Equalities Inequalities = Equals- is the same as Congruent- same size and shape Similar- same.

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