Final answer:
To solve for the absolute values in the equation |2x + 3| - 5 = 0, we first isolate the absolute value, resulting in two possible scenarios. Solving both scenarios gives us the solutions x = 1 and x = -4, which correspond to answer choices A and B respectively.
Step-by-step explanation:
The question asks us to solve for the absolute values of the equation |2x + 3| - 5 = 0. We can approach this by first isolating the absolute value expression:
- Add 5 to both sides of the equation: |2x + 3| = 5.
- There are two scenarios to consider since the absolute value of a number can be both negative and positive inside the absolute value sign. This leads to two separate equations: 2x + 3 = 5 and 2x + 3 = -5.
- For 2x + 3 = 5: Subtract 3 from both sides to get 2x = 2, then divide by 2 to find x = 1.
- For 2x + 3 = -5: Subtract 3 from both sides to get 2x = -8, then divide by 2 to find x = -4.
Therefore, the solutions for x are 1 and -4. Answer choices (A) x = 1 and (B) x = -4 are correct.