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Solving a Linear Inequality

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

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Solving a Linear Inequality

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  1. Solving a Linear Inequality

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

  3. Finding an Inequality Boundary Boundary Point: A solution(s) that makes theinequality 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.

  4. Solving a 1 Variable Inequality Represent the solutions to the following inequality algebraically and on a number line. Closed or Open Dot(s)? Graphical Solution Find the Boundary Test Every Region x Change inequality to equality 0 Pick a point in each region x = 2 x = 0 Solve Substitute into Original 3 < 1 -1 < 1 False True Shade True Region(s) Plot Boundary Point(s) Algebraic Solution

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

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

  7. Solving an Absolute Value Inequality Represent the solutions to the following inequality algebraically and on a number line. Closed or Open Dot(s)? Graphical Solution Find the Boundary Test Every Region x Change inequality to equality 0 Pick a point in each region Solve x = 6 x = 0 x = -2 Substitute into Original 2 > 3 4 > 3 4 > 3 False True True Shade True Region(s) Algebraic Solution Plot Boundary Point(s)

  8. Solving a Quadratic Inequality Represent the solutions to the following inequality algebraically and on a number line. Closed or Open Dot(s)? Graphical Solution Find the Boundary Test Every Region x Change inequality to equality 0 Pick a point in each region Solve x = 2 x = 0 x = -4 Substitute into Original 1 < 4 9 ≤4 9 < 4 True False False Shade True Region(s) Algebraic Solution Plot Boundary Point(s)

  9. Solving a 1 Variable Inequality Represent the solutions to the following inequality algebraically and on a number line. Closed or Open Dot(s)? Graphical Solution Find the Boundary Test Every Region x Change inequality to equality 0 Pick a point in each region Solve x = 3 x = 0 x = -4 Substitute into Original -3 ≤ 3 30 ≤ 24 9 ≤ 3 True False False Shade True Region(s) Algebraic Solution Plot Boundary Point(s)

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