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  4. Assertion: The inequality ax + by < 0 is strict inequality. Reason: The inequality ax + b ≥ 0 is slack inequality.

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Q. Assertion : The inequality $ax + by < 0$ is strict inequality.
Reason : The inequality $ax + b \geq 0$ is slack inequality.

Linear Inequalities

Solution:

Let us consider some inequalities:
$ax + b < 0 \ldots$ (i)
$a x+b > 0 \ldots$(ii)
$a x+b \leq 0 \ldots $ (iii)
$a x+b \geq 0 \ldots$ (iv)
$a x+b y > c \ldots $ (v)
$a x+b y \leq c \ldots$(vi)
$ax ^{2}+ bx + c > 0 \ldots$(vii)
$a x^{2}+b x+c \leq 0 \ldots$ (viii)
Inequalities (i), (ii), (v) and (vii) are strict inequalities, while inequalities (iii), (iv), (vi) and (viii) are slack inequalities.
$\therefore $ Both Assertion and Reason are correct but Reason cannot explain Assertion.