Essential Questions Why is an inequality so important

Essential Questions Why is an inequality so important in the real world? When is it important to know the benefits of solving inequalities in order to be able to qualify for a certain situation in your life?

Unit Questions How do we solve linear inequalities? How do we graph linear inequalities? How do we solve systems of linear inequalities?

SOLVING AND GRAPHING INEQUALITIES Annette Glover

Outline: Solving Inequalities q Graphing Inequalities q Solving Systems of Inequalities by Graphing q Solving Real-World Problems with Inequalities q ≤ ≥ < >

To Solve an Inequality: Solve for y. Example: 2 x-3 y≤ 12 -3 y≤-2 x+12 **Divide by -3 and remember that when you divide by a negative your inequality sign changes. Y≥(2/3)x-4 -4 is the y-intercept 2/3 is the slope (rise over run)

To Graph an Inequality: v. If y is “less than” (<), the graph line is dotted and is shaded under v. If y is “greater than” (>), the graph line is dotted and is shaded above v. If y is “less than or equal to” (≤), the graph line is solid and is shaded v. If y is “greater than or equal to” (≥), the graph line is solid and is shaded above

To Graph an Inequality (Cont. ): Let’s use the inequality we just solved. Y≥(2/3)x-4 ; -4 is the y-intercept 2/3 is the slope (rise over run)

Solving Inequality Systems by Graphing: Let’s use the inequality we just solved Y≥(2/3)x-4 and also graph x≥ 1 Remember: x “less than” (<) is a dotted vertical line and shaded to the left x “greater than” (>) is a dotted vertical line and shaded to the right x “less than or equal to” (≤) is a solid vertical line shaded to the left x “greater than or equal to” (≥) is a solid vertical line shaded to the right

Solving Inequality Systems by Graphing (Cont. ): The solution is the shaded portion within the two solid lines.

Solving Real-World Problems Using Inequalities: The most popular question in math is, “when will we use this in the real world? ” Here is an example: You have around a $100 to spend definitely no more than that. You want to purchase two pairs of shoes that cost $40 a piece. You want to buy as many pairs of tights that you can with the remaining amount. The tights are $4 a piece. How many pairs of tights can you buy?

Solving Real-World Problems Using Inequalities (Cont. ): To start, you know how much the shoes are and how many you want. You know you have no more than $100 to spend for all of the items. You know that the tights are $4 each, but you don’t know how many you can purchase. We can use “t” to represent the number of tights.

Solving Real-World Problems Using Inequalities (Cont. ): We can set up our inequality as follows: 2($40) + $4 t ≤ $100 $80 + $4 t ≤ $100 - $80 $4 t ≤ $20 t≤ 5 You can buy 5 pairs of tights or less. (tax was not taken into account)

Conclusion: Always solve for y Remember the rules for dotted or solid lines Remember the rules for shading When graphing systems, the solution is the shaded part between the two solid or dotted lines For further assistance, please go to www. purplemath. com

Dr. Holden March 8, 2010