One Variable First Degree Inequalities One Variable First
One Variable First Degree Inequalities
One Variable First Degree Inequality � Written in the form ◦ ax + b ≥ 0 � Solving a first degree inequality in one variable means finding the values of x that make the inequality true ◦ Example: 3 x – 5 ≥ 13 3 x ≥ 13 + 5 x ≥ 18 3 x≥ 6 � 0 6
Representing a Situation � The length of a rectangle is 5 cm more than its width. The perimeter is at least 66 cm. Find the minimum measures of the length and width.
Two Variable First Degree Inequalities
Two Variable First Degree Inequality � Written in the form ◦ ax + by + c = 0 ◦ y = ax + b � The solution set of a first degree inequality in two variables is represented graphically by a halfplane, whose boundry is the equation of the line ◦ Example: ≥ or ≤ Solid boundry > or < Dashed boundry
Example � Represent graphically the solution set for the following inequalities: a) y –x -1< 0 b) -2 x + y + 5 ≥ 0
Example � Translate each of the following graphs into an inequality: a) b) x < -1 y ≤ 2 x -4
Representing the Situation �A financial company employs regular staff at 20$/h and contract staff at 25$/h. The company has a budget of $2000 for the employee salaries.
The cost of using a cell phone varies according to the time of day. One company offers the following rates: 0. 50$/min for 6 am to 8 pm 0. 10$/min for 8 pm to 6 am Jenna receives a bill that is greater than 100. 00$.
�A school bus is transporting both students (s) and teachers (t). Write an expression for each: ◦ There at least 40 people on the bus ◦ There are less than 55 people on the bus ◦ The difference between the number of students and teachers is greater than 30 ◦ There is at least 5 times more students than teachers
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