Pre-Algebra Chapter 2 Solving One-Step Equations and Inequalities
Jan 12, 2016
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