Which of the following statements is true? (r is a positive integer) 1. If p ≥ q, then −p/r ≤ −q/r 2. If p ≤ q, then pr ≥ qr 3. If p > q, then −pr > −qr 4. If p q − r

⇒ p q Since, r is positive so -r will be negative. Dividing by -r on both sides we get, (As on dividing by negative number the sign reverses.) is true. Hence, Option 1 is the correct option.

Mathematics

Which of the following statements is true? (r is a positive integer)
If p ≥ q, then $-\dfrac{p}{r} \le -\dfrac{q}{r}$
If p ≤ q then pr ≥ qr
If p > q, then -pr > -qr
If p < q then p - r > q - r

Linear Inequations

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Answer

⇒ p ≥ q

Since, r is positive so -r will be negative.

Dividing by -r on both sides we get,

$\Rightarrow -\dfrac{p}{r} \le - \dfrac{q}{r}$ (As on dividing by negative number the sign reverses.)

$\therefore -\dfrac{p}{r} \le -\dfrac{q}{r}$ is true.

Hence, Option 1 is the correct option.

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Mathematics

Which of the following statements is true? (r is a positive integer)
If p ≥ q, then $-\dfrac{p}{r} \le -\dfrac{q}{r}$
If p ≤ q then pr ≥ qr
If p > q, then -pr > -qr
If p < q then p - r > q - r

Linear Inequations

Answer

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Mathematics

Which of the following statements is true? (r is a positive integer)If p ≥ q, then −pr≤−qr-\dfrac{p}{r} \le -\dfrac{q}{r}−rp​≤−rq​If p ≤ q then pr ≥ qrIf p > q, then -pr > -qrIf p < q then p - r > q - r

Linear Inequations

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Which of the following statements is true? (r is a positive integer)
If p ≥ q, then $-\dfrac{p}{r} \le -\dfrac{q}{r}$
If p ≤ q then pr ≥ qr
If p > q, then -pr > -qr
If p < q then p - r > q - r

Which of the following is the solution set of x ≤ 3 when the replacement set is the set of integers?
{0, 1, 2, 3}
{……,-2,-1, 0, 1, 2}
{………..,-2,-1, 0, 1, 2, 3}
{…..,-2,-1, 1, 2, 3 }

Which of the following statements is not true ? (r is a positive integer)
If p < q then p - r < q - r
If p ≥ q then -pr ≥ -qr
If p > q, then $\dfrac{p}{r} \gt \dfrac{q}{r}$
If p ≤ q then p + r ≤ q + r

Graphical representation of following inequation on the number line is {x : -3 < x < 2, x ∈ I}
1.
2.
3.
4.

Which of the following is the correct graphical representation of {x : x < 1, x ∈ I} on the number line?
1.
2.
3.
4.