Question

Which of the following is the solution to 4 | X+32 8 ?

Option 1: X=5-5 or X=2-1
Option 2: X=2-1
Option 3: X=-5 or X=-1
Option 4: -5 and X=2

Answer 1

The correct solutions to the equation 4 |x + 32| = 8 are x = -30 and x = -34. None of the provided options is correct.

Step-by-step explanation:

To solve the absolute value equation 4 |x + 32| = 8, we can first isolate the absolute value expression by dividing both sides of the equation by 4, resulting in |x + 32| = 2. The absolute value equation |x + 32| = 2 can be split into two separate equations: x + 32 = 2 and x + 32 = -2.

For the equation x + 32 = 2, we apply the rule that to solve an equation, you can add or subtract the same number on both sides without changing the equality. Subtracting 32 from both sides gives us x = 2 - 32, which simplifies to x = -30.

For the equation x + 32 = -2, we also subtract 32 from both sides to get x = -2 - 32, which simplifies to x = -34.

Therefore, the solutions to the equation 4 |x + 32| = 8 are x = -30 and x = -34, which means Option 3: x = -5 or x = -1 is incorrect, and the correct solution is not provided in the options listed.