Lesson 3-4 Solving Multi-Step Inequalities

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Lesson 3-4Solving Multi-Step Inequalities

• Objectives To solve multi-step inequalities
  with the variable on one and/or both sides.

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Real-World Connection

• Have you ever made or needed a banner? Are you
  into carpentry? Solving multi-step equations can
  help you determine the measurements needed for
  making and building things.

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STEPS

1. Simplify. (Get rid of parentheses, fractions, or
   decimals, combine like terms, etc.)
2. Undo addition or subtractions.
3. Undo multiplication or division. Note Dont
   forget to reverse the symbol if mult/div by a
   negative.
4. Check.

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Example 1, page 153

• a) -3x - 4 lt 14

• b) 5 lt 7 2t

Solution x gt -6

• Solution t lt 1

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Example 1 continued

• c) -8 lt 5n - 23

• d) 5k 12 lt 2

Solution n gt 3
Solution k lt -2
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Example 2, page 154

• To make a second banner, the committee decided to
  make the length 12 feet. They have 40 feet of a
  second type of trim. Write and solve an
  inequality to find the possible widths of the
  second banner.

Solution w lt 8
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Example 3, page 153

• a) 4p2(p 7)lt 9

• b) 15lt 5-2(4m7)

Solution m lt -3
Solution p lt -1
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Example 3, continued

• c) 8 gt 3(5 - b) 2

Solution b gt 3
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Examples 4 5, page 155

• Ex. 4) 3b12 gt 272b

• Ex. 5) -6(x-4)gt7(2x-3)

Solution x lt 2.25
Solution b gt 3
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Summary

• What did you learn today?

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SUMMARY

• Solve multi-step inequalities just as you would
  solve multi-step equations.
• Simplify.
• Undo add/subt.
• Undo mult/div. (Reverse symbol, if needed.)
• Check.

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ASSIGNMENT

• 3-4, page 155,
• Odd 1 79, odd 87-103