Inequalities

1
Inequalities

• Review and Use 1.6(1)

2
Before we begin Interval Notation

• See a pattern? What do these look like
  graphed on a number line?

3
Inequalities and negative numbers

• Solve the following

4
Inequalities and negative numbers

• Solve the following
• How would you test your answer?

Remember, in general, if and
, then and
5
Solving a continued inequality

• Solve. Note, this statement can be worked as two
  parts but it is true only if both parts are true.

What does this solution set look like in interval
notation? Graphed on a number line?
6
Solving a continued inequality

• Solve. Note, this statement can be worked as two
  parts but it is true only if both parts are
  true.
• You can check this on CAS.

7
Rational inequalities and 0

• Solve this inequality, but be careful

8
Rational inequalities and 0

• The only way this statement can be true is if the
  denominator is positive.

9
Rational inequalities and 0

• What does the graph of y 1/(x-2) look like?
  Where is y positive?
• Graph it on CAS.

10
Rational inequalities and 0

• What does the graph of y 1/(x-2) look like?
  Where is the vertical asymptote? Where is y
  positive?

11
Inequalities and absolute value

• Remember, two parts for each of these.

Which one is and and which one is or?
What do the solutions set look like in interval
notation and on the number line?
12
Inequalities and absolute value

• This one is and because it is bounded on each
  end.
• Notice how we change the sign and change the
  direction to get the second statement.

13
Inequalities and absolute value

• This one is and because it is bounded on each
  end.
• We could write this in terms of two overlapping
  intervals, but the combined interval is more
  efficient.

14
Inequalities and absolute value

• This one is or because the solution set opens
  out on each end.

15
And remember

• And the first test next week.