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Exercise 9 · Q10

Q.If p>qp > q and r<0r < 0, then which of the following is true?

(i) pr<qrpr < qr
(ii) p−r<q−rp - r < q - r
(iii) p+r<q+rp + r < q + r
(iv) None of these
Ladakh CbseNCERTSubjective· 1mImportance★★★★★est
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Multiplying p>qp>q by a negative number rr reverses the inequality to pr<qrpr<qr, while adding/subtracting rr preserves the order; hence only option (i) is correct.

Rules of inequalities: for p>qp>q,

  • adding/subtracting the same number keeps the sign: p±r>q±rp\pm r > q\pm r;
  • multiplying by a negative number reverses the sign: if r<0r<0, then pr<qrpr < qr.
  1. Given: p>qp > q and r<0r < 0.
  2. Test (i) pr<qrpr < qr: multiply p>qp>q by r<0r<0 → sign reverses → pr<qrpr < qr. True.
  3. Test (ii) p−r<q−rp-r < q-r: subtracting rr preserves order → p−r>q−rp-r > q-r, so this is false. …

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