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  • Roma
  • Community Manager
2013-07-20T21:45:51+02:00

3|2x-3|-20=4 \\\ 3|2x-3|=4+20 \\\ 3|2x-3|=24 \ /:3 \\\ |2x-3|=8 \\\ 2x-3=8 \ \vee \ 2x-3=-8 \\\ 2x=8+3 \ \vee \ 2x=-8+3 \\\ 2x=11 \ /:2 \ \vee \ 2x=-5 \ /:2 \\\ x=5,5 \ \vee \ x=-2,5

 

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|x|+|x+1|=7 \\\ |x+1|=7 - |x| \\\ 7 - |x| \geq 0 \ \wedge \ [ x + 1 = 7 - |x| \ \vee \ x+1 = -(7 - |x|)] \\\\ 7 - |x| \geq 0 \\\ -|x| \geq - 7 \ / \cdot (-1) \\\ |x| \leq 7 \\\ x \leq 7 \ \wedge \ x \geq - 7 \\\ Zatem: x \in \langle -7; \ 7 \rangle \\\\ x + 1 = 7 - |x| \ \vee \ x+1 = -(7 - |x|) \\\ |x| = -x+6 \ \vee \ |x| = x +1+ 7 \\\ |x| = -x+6 \ \vee \ |x| = x +8 \\\ x = -x+6 \ \vee \ x = -(-x+6) \ \vee \ x = x + 8 \ \vee \ x = -(x +8) \\\\ x = -x +6 \\\ x+x = 6 \\\ 2x = 6 \ /:2 \\\ x = 3

 

x = -(-x+6) \\\ x = x -6 \\\ x - x = - 6 \\\ 0 = - 6 \ \ (nieprawda) \\\\ x = x + 8 \\\ x - x = 8 \\\ 0 = 8 \ \ (nieprawda) \\\\ x = -(x +8) \\\ x = - x - 8 \\\ x+x = - 8 \\\ 2x = - 8 \ /:2 \\\ x = - 4 \\\\ Zatem: \\\ x = 3 \ \vee \ x = - 4, \ czyli \\\ x \in \{-4; \ 3\}

 

Ostatecznie:

x \in \langle -7; \ 7 \rangle \cap \{-4; \ 3\} = \{-4; \ 3\} \\\\ Zatem: \ x = - 4 \ \vee \ x = 3