Math 2303 Section 3.2 Section 3.2: Equations and Inequalities Definition: An equation is mathematical statement which equates two algebraic expressions. An equation consists of a left‐hand side, a right hand side, and an equal sign. Definition: If an equation contains a variable (or variables), then a solution of the equation is the value of the variable (or set of values of the variables) which make the equation true. 4
Example 1: Which of the following values are solutions of the equations: 3. a. x =1 b. x = 2 c. x = 3 Example 2: Determine if x =2 is a solution of the equation: 9
14
4 Example 3: Determine of the pair of values x= 3, y = 1 is a solution of the equation. 4
2
10 1 Math 2303 Section 3.2 An inequality is a mathematical statement which connects two algebraic expressions with one of the following symbols:  < “less than”  “ less than or equal to”  > “greater than”  “greater than or equal to”  ”not equal” Definition: If an inequality contains a variable (or variables), then a solution of the inequality is a value of the variable (or set of values of the variables) which make the inequality true. Example 4: Determine if the pair of values 1, 6 is a solution of the inequality: 5
4, 3 is a solution of the inequality: 3
3 Example 5: Determine if the pair of values 7
2
5
16 Example 6: Determine if the pair of values 2
3
0, 2 is a solution of the inequality: 6 2