Gina Wilson All Things Algebra Unit 2 Equations And Inequalities

Unit 2 covers solving linear equations and inequalities, plus graphing solution sets.

Key Concepts

• Concept: Linear equations in one variable
• Concept: Isolating the variable
• Concept: Solution sets for inequalities
• Concept: Graphing solutions on a number line

Steps

1. Action: Identify equation type
2. Action: Apply inverse operations to isolate x
3. Action: Check solution by substitution
4. Action: Graph solution on number line

Formula

$$x = frac{c – b}{a} quad (a neq 0)$$

For inequalities (a > 0):
$$ax + b < c Rightarrow x < frac{c - b}{a}$$ $$ax + b le c Rightarrow x le frac{c - b}{a}$$ $$ax + b > c Rightarrow x > frac{c – b}{a}$$
$$ax + b ge c Rightarrow x ge frac{c – b}{a}$$

If a < 0, the inequality directions reverse.