Solving Nonlinear Inequalities Steps (Multiple Examples)

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Solving Nonlinear InequalitiesSteps (Multiple
Examples)
The following steps can be applied to the
following types of nonlinear inequalities as well
as others. Polynomial Rational Exponential Logarit
hmic Radical (Root) Trigonometric Unfortunately
with showing 6 examples, there isn't enough room
on each slide to show the work from previous
slides. So you may want to note results from
previous slides for the example you're following.
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Solving Nonlinear InequalitiesSteps (Multiple
Examples)
Step 1Related Equation Solve the related
equation to find when both side are equal.
Examples Polynomial Rational Exponential Radical
Logarithmic Trigonometric
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Solving Nonlinear InequalitiesSteps (Multiple
Examples)
Step 2Domain Find domain restrictions to find
out where the inequality is undefined.
Examples Polynomial Rational Exponential Radical
Logarithmic Trigonometric
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Solving Nonlinear InequalitiesSteps (Multiple
Examples)
Step 3Real Line Set up the intervals on a real
line using endpoints from both the solutions to
the related equation and the domain.
Examples Polynomial Rational Exponential Radical
Logarithmic Trigonometric
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Solving Nonlinear InequalitiesSteps (Multiple
Examples)
Step 4Intervals Decide which intervals should
be included based on either a sign graph, test
points, or a calculator's graph. I'll use the
calculator's graph for the examples.
Examples Polynomial Rational Exponential Radical
Logarithmic Trigonometric
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Solving Nonlinear InequalitiesSteps (Multiple
Examples)
Step 5Endpoints For each endpoint, determine
whether it is included or not based on the domain
restrictions, and whether it is a strict
inequality or not.
Examples Polynomial Rational Exponential Radical
Logarithmic Trigonometric
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Solving Nonlinear InequalitiesSteps (Multiple
Examples)
Step 6Solution Set Finally, give the solution
set.
Examples Polynomial Rational Exponential Radical
Logarithmic Trigonometric
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