pre-algebra chapter 2 solving one-step equations and inequalities
TRANSCRIPT
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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 PropertyDraw 2 rectangles with the same width and
different lengths:
5in
3in
5in
11in
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2-2 continued
Draw 2 rectangles with the same width and different lengths:
5in
3in
14in
11in
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2-2 continued
5in
3in
14in
11in
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• 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.
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2-3 Simplifying Variable Expressions
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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.
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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 Subtraction2. Check solution
3. Undo Multiplication or Division4. 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 Subtraction2. Check solution
3. Undo Multiplication or Division4. Check Solution
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2.7 Problem Solving: Guess, Check, Revise
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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.
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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:
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2.9 Solving Inequalities by Adding and Subtracting
• Subtraction Property of Inequality
• Addition Property of Inequality
Also True for ˂, ≤ or ≥.
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 IntegersWhen adding opposites, the sum is zero
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