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

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

3. 2-1 Properties of Numbers
Identity Property of Addition and Multiplication
The Additive Identity is zero.
Multiplicative Identity is one

4. Examples

5. Examples

6. 2-2 The Distributive Property
Draw 2 rectangles with the same width and different lengths:
5in
5in
3in
11in

7. 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

8. 2-2 continued
14in
5in
3in
11in

9. 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.

10. 2-3 Simplifying Variable Expressions

11. 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.

12. 2.5 Solving Equations by Adding and Subtracting
Subtraction Property of Equality
Addition Property of Equality

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

14. 2.6 Solving Equations by Multiplication & Division
Division Property of Equality
Multiplication Property of Equality

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

16. 2.7 Problem Solving: Guess, Check, Revise

17. 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.

18. 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:

19. 2.9 Solving Inequalities by Adding and Subtracting
Subtraction Property of Inequality
Also True for ˂, ≤ or ≥.
Addition Property of Inequality
Also True for ˂, ≤ or ≥.

20. 2.10 Solving Inequalities by Multiplication & Division
Division Property of Inequality
Also True for ˂, ≤ or ≥.
Also True for ˂, ≤ or ≥.

21. 2.10 Solving Inequalities by Multiplication & Division
Multiplication Property of Inequality
Also True for ˂, ≤ or ≥.
Also True for ˂, ≤ or ≥.

22. Underconstruction

23. 1-5 Adding Integers
When adding opposites, the sum is zero