5 8x4 2 Solve the inequality A x B x C x or x D

5. [8x-4] < 2          Solve the inequality.

            A. ¼ < x < ¾

            B. -¾ < x < -¼

            C. x < -¾ or x > -¼

            D. x < ¼ or x > ¾

Solution

It is presumed that as per the question , the absolute value of (8x -4 ) < 2.

We have 2 options. If 8x - 4 > 0, then 8x - 4 is positive and we have 8x -4 < 2. Adding 4 to both the sides, we have 8x - 4 + 4 < 2 + 4 or, 8x < 6. Dividing both the sides by 6, we have x < 6/8 or, x < 3/4.

However, if 8x - 4 < 0 , then -(8x - 4) is positive and we have -(8x - 4) < 2 or, - 8x + 4 < 2. Adding - 4 to both the sides, we have - 8x + 4 - 4 < 2 + ( - 4) or, - 8x , -2 or, 8x > 2. On dividing both the sides by 8, we have x > 2/8 or x > 1/4 . Thus, the answer is 1/4 < x < 3/4. Thus the correct answer is A.