Solving Multi-Step Inequalities

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Lesson 6-3

• Solving Multi-Step Inequalities

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Objectives

• Solve inequalities involving more than one
  operation
• Solve linear inequalities involving the
  Distributive Property

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Vocabulary

• none

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Multiplication and Division PoE

• Properties of Equality (PoE) are based on the
  concept that as long as you do the same thing to
  both sides of an equation, then you have not
  changed anything.
• Multiplication PoE
• For any numbers a, b, and c, if a b, then ac
  bc
• You can multiply both sides of an equation by the
  same thing without changing the equation
• Division PoE
• For any numbers a, b, and c with c ? 0, if a b,
  then a/c b/c
• You can divide both sides of an equation by the
  same thing without changing the equation
• Multiplication and division are reciprocal actions

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Example 1
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Example 1 cont
Answer Water will be a gas for all
temperatures greater than 100C.
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Example 2
Solve 13 11d 79. Then check your solution.
Check To check the solution, substitute 6, a
number less than 6, and a number greater than
6.
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Example 3
Write an inequality for the sentence below. Then
solve the inequality. Four times a number plus
twelve is less than a number minus three.
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Example 3 cont
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Example 4
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Example 5
Answer Since the inequality results in a
false statement, the solution set is the empty
set Ø.
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Summary Homework

• Summary
• Multi-step inequalities can be solved by undoing
  the operations
• Remember to reverse the inequality sign when
  multiplying or dividing each side by a negative
  number
• When solving equations that contain grouping
  symbols, first use the Distributive Property to
  remove the grouping symbols
• Homework
• Pg 335 16-38 even