Equação 01

por **Fafa** Qui 09 Jun 2011, 18:54

por mcgiorda Qui 09 Jun 2011, 22:40

MÓDULOS:

$|2x-3| = 2x-3 \: \: \left (x\geq \frac{3}{2} \right )$
$|2x-3| = 3-2x \: \: \left (x\leq \frac{3}{2} \right )$

$|-2x+5| = -2x+5 \: \: \left (x\leq \frac{5}{2} \right )$
$|-2x+5| = 2x-5 \: \: \left (x\geq \frac{5}{2} \right )$

$|x| = x \: \: \left (x\geq 0 \right )$
$|x| = -x \: \: \left (x\leq 0 \right )$
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$\large {\color{Blue} para\: \: x\leq 0:}$

$3-2x-2x+5=-x\: {\color{DarkGreen} \rightarrow }\: -3x+8=0$

$\large {\color{Red} x=\frac{8}{3}}$

NÃO CONVÉM!! -> $\large {\color{Blue} para\: \: x\leq 0:}$
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$\large {\color{Blue} para \: \: 0\leq x\leq \frac{3}{2}:}$

$3-2x-2x+5=x\: {\color{DarkGreen} \rightarrow }\: -5x+8=0$

$\large {\color{Red} x=\frac{8}{5}= 1,6}$

NÃO CONVÉM!! -> $\large {\color{Blue} x\leq \frac{3}{2}=1,5}$
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$\large {\color{Blue} para\: \: \frac{3}{2}\leq x\leq \frac{5}{2}}$

$2x-3-2x+5=x\: {\color{DarkGreen} \rightarrow }\: -x+2=0$

$\large {\color{DarkGreen} x=2}$

CONVÉM!!
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$\large {\color{Blue} para \: \: x\geq \frac{5}{2}:}$

$2x-3+2x-5=x\: {\color{DarkGreen} \rightarrow }\: 3x-8=0$

$\large {\color{DarkGreen} x=\frac{8}{3}\simeq 2,7}$

CONVÉM!!

$\large S={\color{Blue} \left \{ 2\: ;\: \frac{8}{3} \right \}}$

Equação 01

Equação 01

Re: Equação 01

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