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Solve each inequality. 1) x - 7 x - 1. < 0. 2) x + 5 x - 4 2. > 0. Critical thinking question: 11) Write a rational inequality with the solution: (-2, -1)?(1, ?) Worksheet by Kuta Software LLC. Kuta Software - Infinite Precalculus. Rational Inequalities. Name___________________________________. Date________________
Rational Functions. 4.3 Rational Inequalities and Applications. In this section, we solve equations and inequalities involving rational functions and explore associ- .. As is common with 'word problems' like Examples 4.3.2 and 4.3.3, there is no short-cut to the answer. We encourage the reader to carefully think through and
18 May 2016 solutions as they can. Inform the class that this lesson provides systematic techniques to solve rational equations and inequalities. the original equation, it is the only solution. Let us apply the concepts we learned in solving rational equations to solving word problems. Rational equations can. 2 / 11. 3 / 12
the inequality. The solution and graph are given below and in Figure 3: 4 x. 2 Inequality notation. (4, 2). Interval notation. Note: If in the original problem had been instead, then we would have included the zeros of the polynomial in the solution set. The steps in the above process are summarized in the following box: x. 4, 2.
Solution. Because the left-hand side can be factored, we can write the inequality as. (x. 5)(x. 2). 0. This inequality says that the product of x. 5 and x. 2 is positive. If both factors are negative or both are positive, the product is positive. To analyze the signs of each factor, we make a sign graph as follows. First consider the
We can now see that the quotient is positive when x < 7 or when x > 3. The same solution can be written in interval notation as ( #,7) $ (3,#). Method 2. (Note that this method only works if one side of the inequality is zero.) This method is based on the fact that the inequalities x + 7 x 3. > 0 and (x + 7) (x 3) > 0 have the same
More Equations and Inequalities. 9.1 Compound Inequalities. 9.2 Polynomial and Rational Inequalities. 9.3 Absolute Value Equations. 9.4 Absolute Value Inequalities If the inequalities are joined by the word or, find the union of the two solution sets. 3. Express the solution set in interval notation or in set-builder notation.
problem. The variety of problems is meant to encompass the scope of typical Algebra II problems. 3. Distribute copies of the attached Steps for Solving Rational Equations Graphically handout, and lead students through the steps in each example, using graphing calculators. 4. Define extraneous solution as a result that is
by crator-avatar Mr. Cruz 3. 32:24; 3; 2 years ago. most-viewed-thumbnail. Solving Word Problems 1. by crator-avatar Mr. Cruz 2. 32:09; 2; 2 years ago. most-viewed-thumbnail. Word Problems - The Basics. by crator-avatar Mr. Cruz 1. 20:47; 1; 2 years ago. most-viewed-thumbnail. Do now 33- inequalities , absolute value,
Notes on Rational Inequalities. To Solve Rational Inequalities: 1. Write the inequality as an equation. 2. Solve the equation. 3. Determine all values that make the denominator zero. 4. Draw a number line, and mark all the solutions and critical values from steps 2 and 3. 5. Select a test point in each interval between the
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