Question

Solve the absolute value equation. | 4 - 8x | = 40 Select the correct choice below and fill in any answer boxes in your choice. A. The solution is x equals =__ ​(Use a comma to separate answers as​ needed.) B. There is no solution.

Answer 1

A. x = 5,5 , -4,5 are the TWO SOLUTIONS of | 4 - 8 x | = 40

Explanation:

Here, the given expression is: | 4 - 8 x | = 40

Now, here firstly we need the find the range where (4-8 x) is NEGATIVE and where (4-8x) is POSITIVE.

To find CRITICAL POINT, put (4-8 x) = 0

⇒ 4 = 8x or x = 4/8 = 1/2

⇒ x = 1/2 is the CRITICAL POINT.

CASE - 1 : For x > 1/2, ( 4-8x) < 0 ( negative)

⇒ for x > 1/2 , | 4 - 8 x | = 40 is -(4- 8x) = 40 ( for a < 0, IaI = -a)

or, -4 + 8 x = 40

or, 8 x = 44 , or x = 44/8 = 5.5

⇒ for x > 1/2, x = 5.5 is the solution of | 4 - 8 x | = 40

CASE - 1 : For x ≤ 1/2, ( 4- 8 x) ≥ 0 ( positive)

⇒ for x ≤ 1/2 , | 4 - 8 x | = 40 is (4- 8x) = 40 ( for a > 0, IaI = a)

or, 4 - 8 x = 40

or, 8 x =4 - 40 , or 8 x = -36 or, x = -36/8 = -4.5

⇒ for x ≤ 1/2, x = -4.5 is the solution of | 4 - 8 x | = 40

Hence, x = 5,5 , -4,5 are the TWO POSSIBLE SOLUTIONS of | 4 - 8 x | = 40