1.specify value absolute x if ? b.∣2x+3∣+x−3=0


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Question Number 109754 by joki last updated on 25/Aug/20

$1 . s p e c i f y v a l u e a b s o l u t e x i f ?$ $b . ∣ 2 x + 3 ∣ + x - 3 = 0$
	Answered by Her_Majesty last updated on 25/Aug/20

	$∣ \frac{3 x + 1}{x - 2} ∣= 1$ $(1) x < - 1 / 3$ $\frac{3 x + 1}{x - 2} = 1 \Leftrightarrow x = - 3 / 2$ $(2) - 1 / 3 ⩽ x < 2$ $- \frac{3 x + 1}{x - 2} = 1 \Leftrightarrow x = 1 / 4$ $(3) 2 < x$ $n o s o l u t i o n$ $\Rightarrow x = - 3 / 2 \lor x = 1 / 4$ $∣ 2 x + 3 ∣ + x - 3 = 0$ $(1) x < - 3 / 2$ $- (2 x + 3) + x - 3 = 0 \Leftrightarrow x = - 6$ $(2) x ⩾ - 3 / 2$ $2 x + 3 + x - 3 = 0 \Leftrightarrow x = 0$ $\Rightarrow x = - 6 \lor x = 0$
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