Solving Linear Inequalities

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Section 6.5
Math in Our World

• Solving Linear Inequalities

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Learning Objectives

• Graph solution sets for simple inequalities.
• Solve linear inequalities in one variable.
• Solve three-part linear inequalities.
• Solve real-world problems using inequalities.

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Linear Inequalities
To solve a linear inequality means to find the
set of all numbers that make the inequality a
true statement when substituted in for the
variable. That set is called the solution set for
the inequality.
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Graphing Inequalities
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EXAMPLE 1 Graphing Solution Sets for Simple
Inequalities

• Graph the solution set for each inequality.
• (a) x 10 (b) y gt 4 (c) 30 lt x 50

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Solving Linear Inequalities
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EXAMPLE 2 Solving a Linear Inequality

• Solve and graph the solution set for 5x 9 21.

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EXAMPLE 3 Solving a Linear Inequality

• Solve and graph the solution set for 16 3x gt 40.

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EXAMPLE 4 Solving a Linear Inequality

• Solve and graph the solution set for
• 4(x 3) lt 2x 26.

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EXAMPLE 5 Solving a Three-Part Linear
Inequality

• Solve and graph the solution set for 4 lt 3 2y
  9.

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Common Phrases in Inequalities
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EXAMPLE 6 Applying Inequalities toVacation
Planning

• With the stress of finals behind you, you decide
  to plan a vacation to relax a little bit. After
  poking around on the Internet, you find a room in
  the area you want to visit for 65 per night.
  Some quick estimating leads you to conclude that
  youll need at least 250 for gas, food,
  beverages, and entertainment expenses. Upon
  checking your bank balance, you decide that you
  can afford to spend at most 600 on the trip. How
  many nights can you stay?

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EXAMPLE 7 Applying Inequalities to the Cost of
Buying Food

• Mike is planning to buy lunch for himself and
  some coworkers. He decides to buy cheeseburgers
  and fries from the value menuthe burgers are 1
  each, and the fries cost 0.80. He also needs to
  pay 5 of the total in sales tax. What is the
  largest number of items he can buy if he wants to
  buy the same number of burgers as fries, and he
  only has 10 to spend?

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Classwork

• p. 326-327 5-53 eoo, 63-71 odd