Final answer:
The given inequality simplifies to a true statement independent of the variable x after canceling out the x terms, which means it has no solution in terms of x. The answer choices provided do not reflect this outcome. This indicates a possible error in the question or answer options.
Step-by-step explanation:
To solve the inequality –3(2x − 5) > −6x + 9, first expand the left side:
- Multiply -3 with both terms inside the parentheses: -3 × 2x gives -6x, and -3 × (-5) gives +15.
- So, -3(2x - 5) becomes -6x + 15.
- The inequality now reads -6x + 15 > -6x + 9.
Next, simplify the inequality:
- Subtract -6x from both sides to get: 15 > 9.
- You notice that the x terms cancel out, and we are left with a statement that does not contain the variable x.
- Since 15 is indeed greater than 9, the inequality holds true for all x, meaning that it has no solution in the context of x, as all values of x will satisfy this inequality.
However, reviewing the provided answer choices, it seems none reflects this outcome. This could either be a typo in the question or a misunderstanding, as the inequality simplifies to a true statement independent of x.
If we had to choose the best possible answer from the provided options despite the apparent issue, we might look at the original inequality before simplification, which indicates that the inequality is dependent on x. Assuming we made a mistake in simplification (although that doesn't seem to be the case), the correct step would involve isolating x and determining its relationship to the constants in the inequality. However, since this question simplifies to a true statement without reference to x, it is better to note that none of the answer options correctly describe the solution to the given inequality.