Algebra I Recipe: Equations and Inequalities
Definitions
1. open sentences - equations or inequalities that contain variables and cannot be answered true or false.
• 2x – 3 = 5 cannot be answered true or false until a value is given for x.

2. equation - is formed when an "equal to" symbol is placed between two expressions.
• is means =

3. inequality - looks like an equation except there is an inequality symbol between two expressions.
• > represents is "greater than"
• < represents is "less than"
• ≥ represents is "greater than or equal to"
• ≤ represents is "less than or equal to"

4. solution – is a number that replaces the variable and makes the open sentence true.
Examples:
 Is a = 5 a solution to 2a + 1 = 11?
 Is a = 5 a solution to 6a – 5 = 15?
 Is a = 5 a solution to 5a + 4 = 26?
 Is a = 5 a solution to 45 ÷ a = 9?
 Is a = 5 a solution to a2 + 2 = 27?
 Is a = 5 a solution to 40/a = 8?
Examples:
 Is b = 8 a solution to 8 ≥ 64 ÷ b?
 Is b = 8 a solution to 3b – 24 > 0?
 Is b = 8 a solution to 16 ≤ b2?
 Is b = 8 a solution to 60 > 7b + 3?
 Is b = 8 a solution to 18 – b < 10?
 Is b = 8 a solution to 37 ≥ 4b?

G Redden

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