Section 1.6 Absolute Value Equations 97 83. Amy knows from reading her syllabus in intermediate algebra that the average of her chapter tests accounts for 80% (0.8) of her overall course grade. She also knows that the final exam counts as 20% (0.2) of her grade. a. Suppose that the average of Amy’s chapter tests is 92%. Determine the range of grades that she would need on her final exam to get an “A” in the class. (Assume that a grade of “A” is obtained if Amy’s overall average is 90% or better.) b. Determine the range of grades that Amy would need on her final exam to get a “B” in the class. (Assume that a grade of “B” is obtained if Amy’s overall average is at least 80% but less than 90%.) 84. Robert knows from reading his syllabus in intermediate algebra that the average of his chapter tests accounts for 60% (0.6) of his overall course grade. He also knows that the final exam counts as 40% (0.4) of his grade. a. Suppose that the average of Robert’s chapter tests is 89%. Determine the range of grades that he would need on his final exam to get an “A” in the class. (Assume that a grade of “A” is obtained if Robert’s overall average is 90% or better.) b. Determine the range of grades that Robert would need on his final exam to get a “B” in the class. (Assume that a grade of “B” is obtained if Robert’s overall average is at least 80% but less than 90%.) 85. The average high and low temperatures for 59 Vancouver, British Columbia, in January are 5.6C and 0C, respectively. The formula relating Celsius temperatures to Fahrenheit temperatures is given by C 1F 322. Convert the inequality 0.0° C 5.6° to an equivalent inequality using Fahrenheit temperatures. 86. For a day in July, the temperatures in Austin, Texas, ranged from 20C to 29C. The formula relating Celsius temperatures to Fahrenheit temperatures is given by C 1F 322. Convert the inequality 20° C 29° to an equivalent inequality using Fahrenheit temperatures. 59 Absolute Value Equations Section 1.6 1. Solving Absolute Value Equations An equation of the form 0x 0 a is called an absolute value equation. For example, consider the equation .From the definition of absolute value, the solutions are found by solving the equations and This gives the equivalent equations and x 4 x 4. Also recall from Section R.3 that the absolute value of a number is its distance from zero on the number line. Therefore, geometrically, the solutions to the 0x 0 4 equation are the values of x that are 4 units from zero on the number line (Figure 1-8). 0x 0 4 x 4 or x 4 x 4 x 4. 0x 0 4 4 units 4 units 4 3 2 1 0 1 2 3 4 Figure 1-8 0x 0 Solving Absolute Value Equations of the Form a If a is a real number, then • If the solutions to the equation • If there is no solution to the equation 0x 0 a 6 0, a. 0x 0 a 0, a are given by x a and x a. Concepts 1. Solving Absolute Value Equations 2. Solving Equations Containing Two Absolute Values
miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above