1. Review of Equations and Inequalities An equation is a mathematical statement that two qualities are equal. Linear Equation in one variable can be written as a x + b = c where a  0. Examples: 5 x – 15 = 02 y – 3 = 7 x = 24 x – 5 = 7

2. Review of Equations and Inequalities To find a solution to these equations, find the value of x that would make this equation true. Find the solution to these. 5 x – 15 = 02 y – 3 = 7 x = 24 x – 5 = 7 Equivalent equations are equations with the same solution set.

3. Review of Equations and Inequalities Examples: 4 x + 3 x + 2 = 23 5 x – 3 x + 8 = 5 + 2 x – 9 + 4 x 7 x + 2 = 2 x – 18 - 3 (y – 3 y) + 4 = -4 (3 y – y) + 6 + 13 y 1 / 3 x – 1 / 9 = 8 / 9 0.09 x + 0.07(25000 – x) = 1930

4. Review of Equations and Inequalities A linear inequality is a statement that describes how two numbers or linear expressions are related to one another. < less than >Greater than  Less than or equal to Greater than or equal to How are the following related? -1 ___ -2(-8 – 2) ____(2 – 3) |-15 + 8| ___ |7 – 13|

5. Review of Equations and Inequalities Set NotationInterval Notation a < x(a,  ) a < x < b(a, b) x < b(- , b) a  x  b[a, b] a  x[a,  ) a < x  b(a, b] a  x < b[a, b) x  b (- , b]

6. Review of Equations and Inequalities A linear inequality in one variable can be written in the form a x + b < c, where a, b, c are real numbers, with a  0. The symbols >, , and  may also be used. Addition Property of Inequality For all real numbers a, b, and c, the inequalities: a < b and a + c < b + c are equivalent.

7. Review of Equations and Inequalities Multiplication Property of Inequality For all real numbers a, b, and c, where c  0, a.the inequalities: a < b and a c < b c are equivalent if c > 0; b.the inequalities: a b c are equivalent if c < 0

8. Review of Equations and Inequalities Examples: