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One Variable First Degree Inequalities

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 : 3x – 5 ≥ 13 3x ≥ 13 + 5

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One Variable First Degree Inequalities

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  1. One Variable First DegreeInequalities

  2. One Variable First DegreeInequality • Written in the form • ax + b ≥ 0 • Solving a first degreeinequality in one variable meansfinding the values of x thatmake the inequalitytrue • Example: 3x – 5 ≥ 13 3x ≥ 13 + 5 x ≥ 18 3 x ≥ 6 0 6

  3. Representing a Situation • The length of a rectangle is 5cm more than its width. The perimeter is at least 66cm. Find the minimum measures of the length and width.

  4. Two Variable First DegreeInequalities

  5. Two Variable First DegreeInequality • Written in the form • ax + by + c = 0 • y = ax + b • The solution set of a first degreeinequality in two variables isrepresentedgraphically by a half-plane, whoseboundryis the equation of the line • Example: ≥ or ≤ Solidboundry > or < Dashedboundry

  6. Example • Representgraphically the solution set for the followinginequalities: a) y –x -1< 0 b) -2x + y + 5 ≥ 0

  7. Example • Translate each of the following graphs into an inequality: a) b) x < -1 y ≤ 2x -4

  8. Representing the Situation • A financialcompanyemploysregular staff at 20$/h and contract staff at 25$/h. The company has a budget of $2000 for the employee salaries.

  9. The cost of using a cell phone varies according to the time of day. One companyoffers the following rates: 0.50$/min for 6am to 8pm0.10$/min for 8pm to 6am Jenna receives a bill thatisgreaterthan 100.00$.

  10. A school bus istransportingbothstudents (s) and teachers (t). Write an expression for each: • There are at least 40 people on the bus • There are lessthan 55 people on the bus • The differencebetween the number of students and teachersisgreaterthan 30 • There isat least 5 times more studentsthanteachers

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