Match List – I with List – II.
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List - I |
List - II |
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(A) The solution set of the inequality $-5 x>3, x \in R$, is |
(I) $\left[\frac{20}{7}, \infty\right)$ |
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(B) The solution set of the inequality is, $\frac{-7 x}{4} ≤ -5, x \in R$ is, |
(II) $\left[\frac{4}{7}, \infty\right)$ |
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(C) The solution set of the inequality $7 x-4 ≥ 0, x \in R$ is, |
(III) $\left(-\infty, \frac{7}{5}\right)$ |
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(D) The solution set of the inequality $9 x-4<4 x+3, x \in R$ is, |
(IV) $\left(-\infty,-\frac{3}{5}\right)$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) - (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
$\text{(A)}\; -5x > 3 \Rightarrow x < -\frac{3}{5}$
$\Rightarrow (-\infty, -\frac{3}{5}) \Rightarrow \text{matches (IV)}$
$\text{(B)}\; \frac{-7x}{4} \le -5 \Rightarrow -7x \le -20 \Rightarrow x \ge \frac{20}{7}$
$\Rightarrow \left[\frac{20}{7}, \infty\right) \Rightarrow \text{matches (I)}$
$\text{(C)}\; 7x - 4 \ge 0 \Rightarrow x \ge \frac{4}{7}$
$\Rightarrow \left[\frac{4}{7}, \infty\right) \Rightarrow \text{matches (II)}$
$\text{(D)}\; 9x - 4 < 4x + 3 \Rightarrow 5x < 7 \Rightarrow x < \frac{7}{5}$
$\Rightarrow (-\infty, \frac{7}{5}) \Rightarrow \text{matches (III)}$
A–IV,\; B–I,\; C–II,\; D–III