Lesson 3 Solving Multi-Step Inequalities

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Lesson 3Solving Multi-Step Inequalities
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Bell RingerSolve the following equations.

1. z 5 lt -5
2. -8 g gt -4
3. -5x lt 25
4. ¾s lt -12

• Did you get
• z lt -10
• g gt 4
• x gt -5
• s lt -16
• If soGREAT JOB!
• If you missed any, check the previous lessons.

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Solving Multi-Step Inequalities

• In order to solve multi-step inequalities, you
  will use more than one operation. It can be
  solved by undoing the operation in the same way
  you would solve an equation with more than one
  operation.

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Heres a Real-World example.

• Ex. 1 Find the temperature in degrees Celsius
  for which chlorine is a gas.
• 9/5 C 32 gt -31
• Firstsubtract 32 from both sides.
• Lastmultiply by the multiplicative inverse of
  9/5.
• 9/5 C 32 gt -31
• -32 -32
• (5/9)9/5 C gt -63 (5/9)
• C gt -35
• Therefore chlorine is a gas when its greater
  than -35C
• Written C, C gt -35

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Definition

• If solving an inequality results in a statement
  that is always true, the solution is all real
  numbers.
• Empty Set, Ø, If solving an inequality
  results in a statement that is never true, the
  solution is the empty set.
• The empty set has no solutions.

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Example of an Empty Set.

• Solve 8(t 2) 3(t - 4) lt 5(t 7) 8
• First, use the distributive property.
• 8t 16 3t 12 lt 5t 35 8
• Now, combine like terms.
• 5t 28 lt 5t 27
• -5t -5t (subtract 5t from both
  sides)
• 28 lt -27
• Since this is a false statement, the solution set
  is the empty set Ø.

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Example 3

• Solve 5x 28 gt 2(2x 7) 10 x
• First, use the distributive property and combine
  like terms.
• 5x 28 gt 4x 14 10 x
• 5x 28 gt 5x 24
• -5x -5x subtract 5x from both
  sides
• 28 gt 24
• Since this is a true statement, the solution is
  all real numbers.