Absolute Value Inequalities Online Tutoring - Maths Tutors

Absolute Value Inequalities Online Tutoring - Maths Tutors Absolute value will always give a positive value that means whether a value is positive or negative but when you take a positive value of that particular number then it will gives a positive value only. Example of absolute value inequalities: - Question 1: - Solve the inequalities | 3 x + 5 | 9. Solution: - If 3 x + 5 0 then | 3 x + 5 | 9 gives, 3 x + 5 9 or, 3 x 4 or, x 4 / 3 (1) Again, if 3 x + 5 0, then | 3 x + 5 | 9 gives - (3 x + 5) 9 or, - 3x 14 or, x - 14 / 3 (2) Therefore from (1) and (2) we get, -14 / 3 x 4 / 3, which is required solution of the given inequalities. Question 2: - If x is an integer and | x + 1 | 3, find x. Solution: - If | x + 1 | 3 then we can write -3 (x + 1) 3 -3 1 x 3 1 - 4 x 2 Question 3: - If x is a real number and | 2 x 7 | 1, find x. Solution: - If | 2 x 7 | 1 then -1 (2 x 7) 1 -1 + 7 2 x 1 + 7 6 2 x 8 3 x 4