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

2-1 Properties of Numbers Commutative Property of Addition and Multiplication Associative Property of Addition & Multiplication

2-1 Properties of Numbers Identity Property of Addition and Multiplication The Additive Identity is zero. Multiplicative Identity is one

Examples

Examples

2-2 The Distributive Property Draw 2 rectangles with the same width and different lengths: 5in 5in 3in 11in

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

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

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.

2-3 Simplifying Variable Expressions

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.

2.5 Solving Equations by Adding and Subtracting Subtraction Property of Equality Addition Property of Equality

Rules for Solving Equations 1. Undo Addition or Subtraction 2. Check solution 3. Undo Multiplication or Division 4. Check Solution

2.6 Solving Equations by Multiplication & Division Division Property of Equality Multiplication Property of Equality

Rules for Solving Equations 1. Undo Addition or Subtraction 2. Check solution 3. Undo Multiplication or Division 4. Check Solution

2.7 Problem Solving: Guess, Check, Revise

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.

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:

2.9 Solving Inequalities by Adding and Subtracting Subtraction Property of Inequality Also True for ˂, ≤ or ≥. Addition Property of Inequality Also True for ˂, ≤ or ≥.

2.10 Solving Inequalities by Multiplication & Division Division Property of Inequality Also True for ˂, ≤ or ≥. Also True for ˂, ≤ or ≥.

2.10 Solving Inequalities by Multiplication & Division Multiplication Property of Inequality Also True for ˂, ≤ or ≥. Also True for ˂, ≤ or ≥.

Underconstruction

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