Skip to main contentSkip to solution

For the inequality 3−2x≥x−323-2x \geq x-32, which of the following are true?

(A) When x∈Nx \in N (set of natural numbers), the solution set is {1,2,3,…,11}\{1,2,3,\dots,11\}.

(B) When x∈Ix \in I (set of integers), the solution set is {−∞,…,−3,−2,−1,0,1,2,3,…10,11}\{-\infty,\dots,-3,-2,-1,0,1,2,3,\dots 10,11\}.

(C) When x∈Wx \in W (set of whole numbers), the solution set is {0,1,2,3,…,11}\{0,1,2,3,\dots,11\}.

(D) When x∈Rx \in R (set of real numbers), the solution set is (−∞,∞)(-\infty,\infty).

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 1

3−2x≥x−32⇒35≥3x⇒x≤353≈11.673-2x \geq x-32 \Rightarrow 35 \geq 3x \Rightarrow x \leq \frac{35}{3} \approx 11.67.

So for NN the set is {1,…,11}\{1,\dots,11\}, for WW it is {0,1,…,11}\{0,1,\dots,11\}, and for integers it is all integers up to 11: (A), (B), (C) hold.

(D) fails, since over RR the solution is (−∞,353]\left(-\infty,\frac{35}{3}\right], not all of RR.

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question