Unit 3 Solving Inequalities

Solving Linear Equations 1) Simplify both sides of the equation a) Distributive Property (look for parentheses) b) Combine Like Terms that are on the same side 2) Get rid of the variable term from one side (by adding or subtracting from both sides) 3) Undo operations in reverse order a) Undo add/subtract first (add to zero) b) Undo multiply/divide next (divide to positive one) 4) Check answer in original equation

Solving Linear Equations Inequalities 1) Simplify both sides of the equation inequality a) Distributive Property (look for parentheses) b) Combine Like Terms that are on the same side 2) Get rid of the variable term from one side (by adding or subtracting from both sides) 3) Undo operations in reverse order a) Undo add/subtract first (add to zero) b) Undo multiply/divide next (divide to positive one) If you multiply or divide both sides by a negative number, then you must switch the direction of the inequality 4) Check answer in original equation inequality

Solving “between” inequalities  Simplify the center section  Distributive Property  Combine Like Terms  Get the variable all by itself  Whatever you do to one section you must do to all 3 sections  Undo addition/subtraction first  Undo multiplication/division next

Solving “Outside” Inequalities  Treat as 2 separate problems.  Solve the left inequality  Bring down the word “or”  Solve the right ineqaulity

Solving Absolute Value Equations  Get rid of anything outside the absolute value symbols  Get rid of the absolute value symbols  |x| = a becomes x = -a or x = a inside = opposite of number or inside = number note: the absolute value symbols went away  Get rid of anything that was inside the abs. val. symbols

Solving Absolute Value Inequalities  Absolute Value “Less Than” Inequalities become “between” compound inequalities  |x| < a becomes -a < x < a opposite of number < inside < number  Absolute Value “Greater Than” Inequalities become “outside” compound inequalities  |x| > a becomes x a inside number