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 PropertyDraw 2 rectangles with the same width and

different lengths:

5in

3in

5in

11in

2-2 continued

Draw 2 rectangles with the same width and different lengths:

5in

3in

14in

11in

2-2 continued

5in

3in

14in

11in

• Term: Is a number or the product of a number and variable(s).

• Constant: Is a term that has no variable.

2-3 Simplifying Variable Expressions

• 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• Equation: Is a mathematical sentence with and

equal sign.

• Open Sentence:

Is an equation with one or more variables.

Examples: 9+2=11 Numericalx+7=12 Variable

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 Subtraction2. Check solution

3. Undo Multiplication or Division4. 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 Subtraction2. Check solution

3. Undo Multiplication or Division4. Check Solution

2.7 Problem Solving: Guess, Check, Revise

2.8 Inequalities and their graphso Inequality is a mathematical sentence that

contains ˂, ˃, ≤, ≥ or ≠.o Solution to an inequality are any numbers that

make the inequality true.

Keywords that are used for inequalitiesAt 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

• Addition Property of Inequality

Also True for ˂, ≤ or ≥.

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 IntegersWhen adding opposites, the sum is zero