Inequalities

1
Inequalities

• More solution sets, and interval notation (1.6)

2
POD

• Solve for R
• (2x3)(x-5)(x1)2 0
• What do you notice about one of the solutions?

3
POD

• Solve for R
• (2x3)(x-5)(x1)2 0
• x -2/3, 5, -1
• What do you notice about one of the solutions?
  One solution occurs twice we say it has a
  multiplicity of two.

4
Last time it was all about

• equalities. Today we talk about inequalities,
  but the idea is the same we still want the
  values that make the statement true.
• What do these solution sets look like on a number
  line?
• How would they look using interval notation?

5
Last time it was all about

• equalities. Today we talk about inequalities,
  but the idea is the same we still want the
  values that make the statement true.
• The bottom line is interval notation. Notice the
  open and closed brackets.
• What do these solution sets look like on a number
  line?

6
Trick 1 for inequalities

• What happens when we multiply or divide by a
  negative number?
• Give the answer in interval notation.

7
Trick 1 for inequalities

• What happens when we multiply or divide by a
  negative number?
• Give the answer in interval notation.

8
Trick 2 for inequalities

• What about a combined inequality?

9
Trick 2 for inequalities

• What about a combined inequality?

10
Trick 3 for inequalities

• What about absolute value inequalities?

11
Trick 3 for inequalities

• What about absolute value inequalities? There
  are two partsset them up by keeping the sign and
  direction in place for one answer, then changing
  the sign and direction for the second answer.
• Careful! The last one is tricky!