Final answer:
The incorrect representation of the inequality 3(2x - 1) < 24(2x - 3) - 3 is C) A number line with a closed circle on 6 and shading to the left, since it shows values less than or equal to 6, which includes numbers that are not solutions to the inequality.
Step-by-step explanation:
The task is to determine which representation is not a correct way to represent the solution of the inequality 3(2x - 1) < 24(2x - 3) - 3. By solving the inequality, we find:
- Multiply out the brackets: 6x - 3 < 48x - 72 - 3.
- Combine like terms: 6x - 3 < 48x - 75.
- Get all the x terms on one side by subtracting 6x from both sides: -3 < 42x - 75.
- Add 75 to both sides: 72 < 42x.
- Divide both sides by 42: 72/42 < x, which simplifies to x > 1.71 (approximately).
The solution to the inequality is x > 1.71, therefore the correct representation should show x values greater than 1.71.
Based on the options provided:
A) x ≤ 6 and B) 6 ≥ x are equivalent, both indicating that x is less than or equal to 6, which does include solutions to the inequality but also includes values that are not solutions (since the inequality solution is strictly greater than 1.71, not less than or equal to 6).
C) A number line with a closed circle on 6 and shading to the left is incorrect because it shows all values less than or equal to 6, which again is not the exclusive solution to our inequality.
D) A number line with a closed circle on 6 and shading to the right is partially correct as it shows values greater than 6; however, it incorrectly indicates that x can be equal to 6 (closed circle), when the original inequality does not allow for x to be equal to any specific value.
Nevertheless, since the question asks which option is not a way to represent the inequality solution, we must choose the most clear-cut incorrect option. Therefore, the correct answer is C, a number line with a closed circle on 6 and shading to the left, since the actual solution is x values that are greater than 1.71, not less than or equal to 6.