Solving a Linear Inequality

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

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 a 1 Variable Inequality 0 x x = 0 x = 2 3 < 1 -1 < 1 FalseTrue 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 1 Variable Inequality: The Answer is All Numbers 0 x Find the BoundaryTest Every Region Represent the solutions to the following inequality algebraically and on a number line. All Numbers Change inequality to equality Solve Since every value of k satisfies the equation, every Point is a Boundary Point “Algebraic” Solution Closed or Open Dot(s)? Graphical Solution

Solving a 1 Variable Inequality: No Solutions 0 x Find the BoundaryTest Every Region Represent the solutions to the following inequality algebraically and on a number line. No Solution Change inequality to equality Solve Since every value of k satisfies the equation, every Point is a Boundary Point “Algebraic” Solution Closed or Open Dot(s)? Graphical Solution

Solving an Absolute Value Inequality 0 x x = -2 x = 0 x = 6 4 > 3 2 > 34 > 3 True False True 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 Quadratic Inequality 0 x x = -4 x = 0 x = 2 9 < 4 1 < 49 ≤ 4 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 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