Solving Compound Inequalities and Solving Open Sentences Involving Absolute Value

1
Solving Compound Inequalitiesand Solving Open
Sentences Involving Absolute Value

• 6-4
• 6-5

3.0 Students solve equations and inequalities
involving absolute values. 4.0 Students simplify
expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5)
4(x-2) 12. 5.0 Students solve multistep
problems, including word problems, involving
linear equations and linear inequalities in one
variable and provide justification for each step.
Jessica N. Sean P. Lynette B.
2
Vocabulary

• Compound Inequality- Two or more inequalities
  that are connected by the words and or or
• Intersection- the graph of a compound inequality
  containing and the solution is the set of
  elements common to both inequalities
• Union- the graph of a compound inequality
  containing or the solution is a solution of
  either inequality, not necessarily both

3

• Ex.1 graph x lt 3 and x -5
• And means that they intersect or they overlap.
• When you combine them you get your answer.

-6 -5 -4 -3 -2 -1 0 1
2 3 4 5
-6 -5 -4 -3 -2 -1 0 1 2
3 4 5
-6 -5 -4 -3 -2 -1 0 1 2
3 4 5
4

• Or means that you plot them and usually nothing
  intercepts
• Ors have wings
• Graph x 3 or x lt -2

-6 -5 -4 -3 -2 -1 0 1 2
3 4 5
5

• When solving absolute value equations, split into
  2 separate problems (one for the negative and one
  for the positive)
• Solve
• x - 4 6
• x - 4 6 x - 4 -6
• 4 4 4 4
• x 10 or x 2

6

• When solving an absolute value inequality, flip
  the sign for a negative.
• x - 2 5
• x - 2 5 x - 2 -5
• 2 2 2 2
• x 7 or x -3
• , lt and
• , gt or

-3 -2 -1 0 1 2 3 4
5 6 7 8
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• Effects by Sean
• Writing by Jessica
• Background and designs by Lynette