First slide

Introduction to linear inequalities

Question

Solution set of the inequation $x^{2} - 2 x \geq 15$ is

Moderate

A

$(- \infty, 3] \cup [5, \infty)$
B

$(- \infty, - 5] \cup [3, \infty)$
C

$(- \infty, - 3] \cup [5, \infty)$
D

None of these

Solution

The given inequation is $x^{2} - 2 x \geq 15$
$\Rightarrow x^{2} - 2 x - 15 \geq 0$

$\Leftrightarrow$     $(x - 5) (x + 3) \geq 0$

$\Leftrightarrow$     $(x - (- 3)) (x - 5) \geq 0$

$\Leftrightarrow$    either $x \leq - 3$ or $x \geq 5$

$\Leftrightarrow$    $x \in (- \infty, 3] \cup [5, \infty)$

                           $(∵ F o r a < b, (x - a) (x - b) \geq 0 iff either x \leq a o r x \geq b)$

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