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**Solving One-Step Equations and Inequalities**

Pre-Algebra Chapter 2 Solving One-Step Equations and Inequalities

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**2-1 Properties of Numbers**

Commutative Property of Addition and Multiplication Associative Property of Addition & Multiplication

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**2-1 Properties of Numbers**

Identity Property of Addition and Multiplication The Additive Identity is zero. Multiplicative Identity is one

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Examples

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Examples

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**2-2 The Distributive Property**

Draw 2 rectangles with the same width and different lengths: 5in 5in 3in 11in

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**Draw 2 rectangles with the same width and different lengths:**

2-2 continued Draw 2 rectangles with the same width and different lengths: 14in 5in 3in 11in

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2-2 continued 14in 5in 3in 11in

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**2-3 Simplifying Variable Expressions**

Term: Is a number or the product of a number and variable(s). Constant: Is a term that has no variable. Like Terms: Terms that have exactly the same variables. Coefficients: Is a number that multiplies the variable.

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**2-3 Simplifying Variable Expressions**

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**2.4 Variables and Equations**

Is a mathematical sentence with and equal sign. Examples: 9+2=11 Numerical x+7=12 Variable Open Sentence: Is an equation with one or more variables. All equations with variable are open.

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**2.5 Solving Equations by Adding and Subtracting**

Subtraction Property of Equality Addition Property of Equality

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**Rules for Solving Equations**

1. Undo Addition or Subtraction 2. Check solution 3. Undo Multiplication or Division 4. Check Solution

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**2.6 Solving Equations by Multiplication & Division**

Division Property of Equality Multiplication Property of Equality

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**Rules for Solving Equations**

1. Undo Addition or Subtraction 2. Check solution 3. Undo Multiplication or Division 4. Check Solution

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**2.7 Problem Solving: Guess, Check, Revise**

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**2.8 Inequalities and their graphs**

Inequality is a mathematical sentence that contains ˂, ˃, ≤, ≥ or ≠. Solution to an inequality are any numbers that make the inequality true.

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**Keywords that are used for inequalities**

At most means ‘no more than’ hence ≤. At least means ‘no less than’ hence ≥. Graphs of Inequalities Ο is used for graphing ˂ or ˃. ● is used for graphing ≤ or ≥. Examples:

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**2.9 Solving Inequalities by Adding and Subtracting**

Subtraction Property of Inequality Also True for ˂, ≤ or ≥. Addition Property of Inequality Also True for ˂, ≤ or ≥.

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**2.10 Solving Inequalities by Multiplication & Division**

Division Property of Inequality Also True for ˂, ≤ or ≥. Also True for ˂, ≤ or ≥.

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**2.10 Solving Inequalities by Multiplication & Division**

Multiplication Property of Inequality Also True for ˂, ≤ or ≥. Also True for ˂, ≤ or ≥.

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Underconstruction

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1-5 Adding Integers When adding opposites, the sum is zero

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