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42 Algebra II Essentials For Dummies The two solutions you come up with are x = 2 and x = 34. Both have to be checked in the original equation. When x = 2, When x = 34, The solution x = 2 works. The other solution, x = 34, doesn’t work in the equation. The number 34 is an extraneous solution. Dealing with Negative Exponents Equations with negative exponents offer some unique challenges. In general, negative exponents are easier to work with if they disappear. Yes, as wonderful as negative exponents are in the world of mathematics, solving equations that contain them is often easier if you can change the format to positive exponents and fractions and then deal with solving the fractional equations (as shown in the previous section).
No matter what numbers you choose in the interval between –3 and 4, the result is always negative because you have a negative times a positive. The complete solution lists both intervals that have working values in the inequality. The solution of the inequality x2 – x > 12, therefore, is x < –3 or x > 4. Signing up for fractions The sign-line process (see the introduction to this section and the previous example problem) is great for solving rational inequalities, such as . The signs of the results of multiplication and division use the same rules, so to determine your answer, you can treat the numerator and denominator the same way you treat two different factors in multiplication.
Zeros are the values of x that make each factored expression equal to 0. 4. Put the zeros in order on a number line. 5. Create a sign line to show where the expression in the inequality is positive or negative. A sign line shows the signs of the different factors in each interval. If the expression is factored, show the signs of the individual factors. 6. Determine the solution, writing it in inequality notation or interval notation (see Chapter 2). Keeping it strictly quadratic The techniques you use to solve the inequalities in this section are also applicable for solving higher-degree polynomial inequalities and rational inequalities.