Page 66

miller_intermediate_algebra_4e_ch1_3

106 Chapter 1 Linear Equations and Inequalities in One Variable Isolate the absolute the form 0x 0 value.The inequality is in 7 a, where a is negative.An absolute value of any real number is greater than a negative number.Therefore, the solution is all real numbers. b. 3d 5 0 7 7 4 0 3d 5 0 7 3 0 All real numbers, 1, 2 Skill Practice Solve the inequalities. 3. ƒ 4p 2 ƒ 6 6 2 4. ƒ 4p 2 ƒ 6 7 2 Example 4 b. 04x 2 0 04x 2 0 04x 2 0 7 0 0 0 04x 2 0 0 An absolute value will be greater than zero at all points except where it is equal to zero.That is, the point(s) for which must be excluded from the solution set. The second equation is the same as the first. Therefore, exclude from the solution. 4x 2 0 or 4x 2 0 5x 0 x 12 6 4x 2 The solution is or equivalently in interval notation, c. 1, 12 2 ´ 1 04x 2 0 0 12 , 2. x An absolute value of a number cannot be less than zero. However, it can be equal to zero.Therefore, the only solutions to this inequality are the solutions to the related equation: e From part (b), we see that the solution set is . Skill Practice Solve the inequalities. 5. ƒ 3x 1 ƒ 0 6. ƒ 3x 1 ƒ 7 0 7. ƒ 3x 1 ƒ 0 1 2 04x 2 0 f 0 12 x 1 2 04x 2 0 0 04x 2 0 0 04x 2 0 7 0 Solving Absolute Value Inequalities Solve the inequalities. a. b. c. Solution: a. The absolute value is already isolated. The absolute value of any real number is nonnegative.Therefore, the solution is all real numbers, 1, 2. (( 1 0 1 2 3 4 5 6 6 5 4 3 2 12 Answers 3. No solution, 4. All real numbers; 5. 6. or , e x | x b 7. e 1 3 f a, 1 3 b ´ a1 3 1 3 f 1, 2 1, 2 5 6


miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above