Graphing and Solving Inequalities

Finding an Inequality Boundary Boundary Point: A solution(s) that makes the inequality true (equal). It could be the smallest number(s) that make it true. Or it is the largest number(s) that makes it NOT true. EX: Find the boundary point of To find a boundary replace the inequality symbol with an equality symbol.

Solving an Inequality In order to find the points that satisfy an inequality statement: 1. Find the boundary 2. Test every region to find which one(s) satisfies the original statement

Reminder: Compound Inequalities The following are examples to algebraically write the following graphs: 0 4 0≤x< x 2

Solving a 1 Variable Inequality 0 x x = -4 x = 0 x = 3 9 ≤ 3 -3 ≤ 330 ≤ 24 False True False Find the BoundaryTest Every Region Represent the solutions to the following inequality algebraically and on a number line. Change inequality to equality Solve Plot Boundary Point(s) Pick a point in each region Substitute into Original Shade True Region(s) Algebraic Solution Closed or Open Dot(s)? Graphical Solution

Solving a 2 Variable Inequality (0,0) Graphically represent the solutions to the following inequality. Find the Boundary Plot points for the equality Test Every Region (3,0) 0 > -3 0 > 1.5 True False Solid or Dashed? Pick a point in each region Substitute into Original Shade True Region(s)

Reminder: Cover-Up Method Plot : -2x + 5y = -10 Find the intercepts XY If the graph is in Ax+By=C form.

Solution to a System of Inequalities A solution to a System of Inequalities is the coordinate(s) that makes ALL of the inequalities true. The graph of all the points that make the system true is called the Feasible Region. EX: Prove (-4,5) is a solution to the system below It must make EVERY inequality true. True

Solving a System of Inequalities (0,0) 0 ≥ -3 True (0,0) 0 < 3 True Test Every Region Graphically represent the solutions to the following system of inequalities: Find the Boundaries Plot points for the equalities one at a time Solid or Dashed? Find which side to shade for each inequality Shade the Feasible Region