Final answer:
The solution to the inequality 8(6x - 7) < 12 is x < 1.4167. If there was a typo and the real inequality should be 8(6x - 7) < 48, then the solution would be x < 2.1667, which is closest to the option x < 20 (Option D).
Step-by-step explanation:
To solve the inequality 8(6x - 7) < 12, we first expand and simplify the inequality. Dividing both sides of the inequality by 8 gives us 6x - 7 < 1.5. Adding 7 to both sides yields 6x < 8.5. Finally, dividing both sides by 6 results in x < 1.4167, which is not given in the listed options (B, C, D). Therefore, the inequality representing all the solutions is different from the options provided.
However, if there was a typo in the original question and the student meant to ask which inequality represents the solution to 8(6x - 7) < 48 (rather than 12), then the solution is as follows:
First, we simplify by dividing both sides by 8, which results in 6x - 7 < 6. Then, we add 7 to both sides to obtain 6x < 13. Lastly, by dividing both sides by 6 we get x < 2.1667. In this case, since none of the answer choices exactly match this result, we assume that the closest correct answer choice would be x < 20 (Option D).