Docstoc

1.6 Solving Compound Inequalities

Document Sample
1.6 Solving Compound Inequalities Powered By Docstoc
					1.6 Solving Compound
     Inequalities
   Understanding that conjunctive
  inequalities take intersections of
intervals and disjunctive inequalities
       take unions of intervals
Part 1: First Box of the Worksheet


Part 1 of the presentation will go over
 completing the first box of the worksheet:

“Understanding conjunctive compound
  inequalities…”
1. Solve the following inequality and sketch
        the interval that satisfies it:

           4  6  2x  4
1. Solve the following inequality and sketch
             the interval that satisfies it:

                  4  6  2x  4
Subtract 6 from each component of the equation…

                    10  2x  2
1. Solve the following inequality and sketch
              the interval that satisfies it:

                   4  6  2x  4
Subtract 6 from each component of the equation…

                     10  2x  2
Divide each component by -2 …remembering to switch the signs.

                         5  x 1
1. Solve the following inequality and sketch
              the interval that satisfies it:

                   4  6  2x  4
Subtract 6 from each component of the equation…

                     10  2x  2
Divide each component by -2 …remembering to switch the signs.

                          5  x 1
                     Or   1 x  5
1. Solve the following inequality and sketch
                the interval that satisfies it:

                        4  6  2x  4
Subtract 6 from each component of the equation…

                        10  2x  2
Divide each component by -2 …remembering to switch the signs.

                             5  x 1
                        Or   1 x  5
Sketch the interval:
   2-4. A conjunctive inequality is the
      intersection of two intervals.

 2. Solve and sketch the interval.
                4  6  2x




3. Solve and sketch the interval.
                  6  2x  4
   2-4. A conjunctive inequality is the
      intersection of two intervals.

 2. Solve and sketch the interval.
                   4  6  2x
     Subtract 6
                   10  2x




3. Solve and sketch the interval.
                    6  2x  4
   2-4. A conjunctive inequality is the
      intersection of two intervals.

 2. Solve and sketch the interval.
                   4  6  2x
     Subtract 6
                     10  2x
      Divide by -2
                      5 x

3. Solve and sketch the interval.
                     6  2x  4
   2-4. A conjunctive inequality is the
      intersection of two intervals.

 2. Solve and sketch the interval.
                   4  6  2x
     Subtract 6
                       10  2x
      Divide by -2
                        5 x
                  Or
                         x5
3. Solve and sketch the interval.
                       6  2x  4
   2-4. A conjunctive inequality is the
      intersection of two intervals.

 2. Solve and sketch the interval.
                   4  6  2x
     Subtract 6
                       10  2x
      Divide by -2
                        5 x
                  Or
                         x5
3. Solve and sketch the interval.
                       6  2x  4
   2-4. A conjunctive inequality is the
      intersection of two intervals.

 2. Solve and sketch the interval.
                    4  6  2x
     Subtract 6
                        10  2x
      Divide by -2
                         5 x
                   Or
                          x5
3. Solve and sketch the interval.
                        6  2x  4
      Subtract 6         2x  2
       Divide by -2        x 1
 2-3. Solve and sketch each of the two
        inequalities separately.

 2. Solve and sketch the interval.
                    4  6  2x
     Subtract 6
                        10  2x
      Divide by -2
                         5 x
                   Or
                          x5
3. Solve and sketch the interval.
                        6  2x  4
      Subtract 6         2x  2
       Divide by -2        x 1
4. The solution to the compound inequality is the
intersection of each separate inequality.

Each inequality separately:

    4  6  2x


     6  2x  4
4. The solution to the compound inequality is the
intersection of each separate inequality.

Each inequality separately:

    4  6  2x


     6  2x  4
Taking the intersection means considering points that satisfy
BOTH inequalities. The first inequality needs to be true and
the second one needs to be true.
    4  6  2x
      AND
    6  2x  4
4. The solution to the compound inequality is the
intersection of each separate inequality.

Each inequality separately:

    4  6  2x


     6  2x  4
Taking the intersection means considering points that satisfy
BOTH inequalities. The first inequality needs to be true and
the second one needs to be true.
    4  6  2x
      AND
    6  2x  4
 Part 1: First Box of the Worksheet

The point of this exercise is that you can solve the
   conjunctive compound inequality in two
   different ways:
1. Solving algebraically by performing operations
   on all 3 parts of the compound inequality.
2. Solve each simple inequality separately and
   then taking the intersection of the two intervals.
  Part 1: First Box of the Worksheet

The point of this exercise is that you can solve the
   conjunctive compound inequality in two
   different ways:
1. Solving algebraically by performing operations
   on all 3 parts of the compound inequality.
2. Solve each simple inequality separately and
   then taking the intersection of the two intervals.

The first way is easier for solving conjunctive
   inequalities. However, disjunctive inequalities can
   only be solved by solving each simple inequality
   separately and then taking their union.
 Part 2: Second Box of the Worksheet


Part 2 of the presentation will go over using
 unions to solve disjunctive compound
 inequalities:

“Solving disjunctive compound inequalities…”
Solve           3x  6 OR x  1  0


1. Solve and sketch the interval.

             3x  6


2. Solve and sketch the interval.

             x 1 0
Solve             3x  6 OR x  1  0


1. Solve and sketch the interval.

                 3x  6
   Divide by 3
                  x  2

2. Solve and sketch the interval.

                 x 1 0
Solve             3x  6 OR x  1  0


1. Solve and sketch the interval.

                 3x  6
   Divide by 3
                  x  2

2. Solve and sketch the interval.

                 x 1 0
Solve             3x  6 OR x  1  0


1. Solve and sketch the interval.

                 3x  6
   Divide by 3
                  x  2

2. Solve and sketch the interval.

                 x 1 0
       Add 1 …
                   x 1
Solve             3x  6 OR x  1  0


1. Solve and sketch the interval.

                 3x  6
   Divide by 3
                  x  2

2. Solve and sketch the interval.

                 x 1 0
       Add 1 …
                   x 1
 Solve          3x  6 OR x  1  0

The ‘or’ means that either the left inequality needs to
be true OR the right inequality needs to be true.
 Solve          3x  6 OR x  1  0

The ‘or’ means that either the left inequality needs to
be true OR the right inequality needs to be true.

Thus, we want all the points that make the left
inequality true together with all the points that make
the right inequality true – we take the union of the two
intervals.




The union is:
 Solve          3x  6 OR x  1  0

The ‘or’ means that either the left inequality needs to
be true OR the right inequality needs to be true.

Thus, we want all the points that make the left
inequality true together with all the points that make
the right inequality true – we take the union of the two
intervals.




The union is:
 Solve           3x  6 OR x  1  0

The ‘or’ means that either the left inequality needs to
be true OR the right inequality needs to be true.

Thus, we want all the points that make the left
inequality true together with all the points that make
the right inequality true – we take the union of the two
intervals.




The union is:
 In interval notation this is: (-∞,2](1, ∞).

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:3
posted:8/18/2012
language:English
pages:29