Solving Inequalities
Solving Inequalities With Algebra
- Rearrange the inequality so right side is 0. Remember Negative Flip. Donāt try to move terms including variables through sides(you dont know if they are negative or positive)
- Find Critical Values of the polynomial
- Draw a number line or Chart
- Pick tests for you number line or chart to find positive or negative values. THINK BIG
Solving Inequalities With Graphing
Critical Values
Critical values are values of x will make f(x) either:
- 0
- Undefined
Chart Making & Rational Chart Making
Chart Making
For solving inequalities.
Example
-x(1+x) > 0
| test | x < -1 | x = -1 | -1 < x < 0 | x = 0 | x > 0 |
|---|---|---|---|---|---|
| -x(x+1) | - | 0 | + | 0 | - |
| this is very monotonous, if you know Bounce and Cross, than you can just guess. |
Rational Chart Making
Oftentimes a question will ask for intervals of increasing and decreasing intervals. What it asks for is a chart. In this chart you will have included:
- Critical Values The boilerplate chart looks as such:
| Interval | x < ? | ? < x < ? | ? < x < ? | ā¦ | ? < x |
|---|---|---|---|---|---|
| f(x) | +/- | +/- | +/- | +/- | |
| slope | +/- | +/- | +/- | +/- | |
| change in slope | +/- | +/- | +/- | +/- |
We donāt make x = anything. Because you cannot have a change in slope at one point.