Compound Inequality

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Compound Inequality

• Definition two inequalities connected by and
  or or.
• When you use and both inequalities have to be
  true.

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Aquariums need to maintain the right temperature
and pH for their fish to survive. They use
diagrams to determine the right pH, a scale with
values from 0-14 is used.
If we let p represent the value of the pH
scale, we can express the different pH levels by
using inequalities for example, an acid solution
will have a pH level of p greater than of equal
to 0 but less than 7. when considered together,
these two inequalities form a COMPOUND INEQUALITY.
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Draw a Diagram

• Pictures can help you to see the answer to a
  problem.

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EXAMPLE A restaurant can use a diagram to
decide how many tables IT would TAKE for a party
of 36 PEOPLE.
You start by making a guessing. Ten tables will
seat 22 people. If we use an extra table, we can
seat 2 more people. Now you look for a pattern.
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This pattern shows that the restaurant needed 17
tables to seat all 36 people.
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Intersection

• Definition The intersection of two sets A and
  B is the set of elements common to both A and
  B.

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• The intersection can be found by graphing the two
  inequalities to see where the graphs overlap.

• When you use and both inequalities have to be
  true.

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• Example
• Bob lives 20 miles from the rink and Steve lives
  17 miles from the rink.
• We do not know the positions of their homes in
  relation to the rink.
• We need a diagram of the situation.
• S will be the location of the rink.
• Since Steve lives 17 miles from the rink, we can
  draw a circle with a radius of 17. He will live
  somewhere on that circle.
• We can draw another circle with radius of 20 for
  Bobs home.

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Lets examine three possibilities

• Diagrams
• shows the least possibilities.
• shows the greatest possibilites
• to shows yourself that the (3) is always true,
  you may want to sketch a different trangle.

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Union
The union of two sets A and B is the set of
elements contained in both A or B.
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The graph of a compound inequality containing
or is the Union of the graphs of the two
inequalities.