Solution
Solution
+2
Interval Notation
Decimal Notation
Solution steps
Let:
Identify the intervals
Find the signs of the factors of
Find the signs of
Find the signs of
Move to the right side
Subtract from both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Move to the right side
Subtract from both sides
Simplify
Multiply both sides by
Multiply both sides by -1 (reverse the inequality)
Simplify
Move to the right side
Subtract from both sides
Simplify
Multiply both sides by
Multiply both sides by -1 (reverse the inequality)
Simplify
Summarize in a table:
Identify the intervals that satisfy the required condition:
Substitute back
If then
Switch sides
For , if then
Simplify
Use the following trivial identity:
Simplify
Use the following trivial identity:
Simplify
For , if then
Simplify
Use the following trivial identity:
Simplify
Convert element to fraction:
Since the denominators are equal, combine the fractions:
Add similar elements:
Apply the fraction rule:
Simplify
Use the following trivial identity:
Combine the intervals
Merge Overlapping Intervals