Răspuns:
Explicație pas cu pas:
6)
[tex]x+y = (\frac{1}{2} -\frac{1}{3} +\frac{1}{4} -\frac{1}{5} +...+\frac{1}{2010} -\frac{1}{2011}) +(1-\frac{1}{2} +\frac{1}{3}-\frac{1}{4} +\frac{1}{5}-\frac{1}{6} + ... \frac{1}{2009}-\frac{1}{2010})=[/tex]
[tex]=1 + (\frac{1}{2} -\frac{1}{2} )+(-\frac{1}{3} +\frac{1}{3} )+(\frac{1}{4} -\frac{1}{4} )+(-\frac{1}{5} +\frac{1}{5} ) + ... + (\frac{1}{2010} -\frac{1}{2010} )-\frac{1}{2011} =[/tex]
[tex]= 1 + 0 + 0 + 0 + 0 + ... + - \frac{1}{2011} =[/tex]
[tex]= 1 - \frac{1}{2011} =[/tex]
[tex]= \frac{2011}{2011} - \frac{1}{2011} =[/tex]
[tex]= \frac{2011-1}{2011} =[/tex]
[tex]= \frac{2010}{2011}[/tex]
Deci media aritmetica a numerelor x si y este:
[tex]\frac{x+y}{2} = \frac{\frac{2010}{2011}}2} = \frac{1005}{2011}[/tex]
7.
a)
x + 17 = 12
x = 12 - 17
x = -5
b)
3x - 5 = 22
3x = 22 + 5
3x = 27
x = 27/3
x = 9
c)
5x + 4 = 7x + 1
5x - 7x = 1 - 4
- 2x = - 3
2x = 3
x = 3/2
d)
2(x-3) + 1 = 5 - 4(x-2)
2x - 6 + 1 = 5 - 4x + 8
2x - 5 = 13 - 4x
2x + 4x = 13 + 5
6x = 18
x = 18/6
x = 3
e)
[tex]\frac{x}{3} -\frac{x-3}{4} =\frac{x+1}{6}[/tex]
[tex]\frac{4x}{12} -\frac{3(x-3)}{12} =\frac{2(x+1)}{12}[/tex]
[tex]4x -3(x-3) =2(x+1)[/tex]
[tex]4x -3x +9 = 2x +2[/tex]
[tex]x +9 = 2x +2[/tex]
[tex]2x -x= 9 - 2[/tex]
[tex]x = 7[/tex]
f)
[tex]\frac{2}{5}*(\frac{5}{4}x -\frac{5}{6} )=3x -\frac{1}{6}[/tex]
[tex]\frac{2}{5}*\frac{5}{4}x - \frac{2}{5}*\frac{5}{6}=3x -\frac{1}{6}[/tex]
[tex]\frac{x}{2} - \frac{1}{3}=3x -\frac{1}{6}[/tex]
[tex]\frac{3x}{6} - \frac{2}{6}=\frac{6*3x}{6} -\frac{1}{6}[/tex]
[tex]3x- 2=18x -1[/tex]
[tex]3x- 18x = -1 + 2[/tex]
[tex]-15x = 1[/tex]
[tex]x=-\frac{1}{15}[/tex]
g)
[tex]0,(3)x + 1,5 = 1[/tex]
[tex]\frac{1}{3}x + \frac{3}{2} = 1[/tex]
[tex]\frac{2x}{6} + \frac{9}{6} = \frac{6}{6}[/tex]
[tex]2x + 9 = 6\\2x = 6-9\\2x = -3\\x = -\frac{3}{2}[/tex]
h)
[tex]3 + |2x - 1|=5\\|2x - 1\ = 5 - 3\\|2x - 1\ = 2\\\\\left \{{{2x-1=+2} \atop{2x-1=-2}} \right.[/tex]
[tex]2x-1 = 2\\2x = 2 + 1 \\2x = 3\\x = \frac{3}{2}[/tex]
[tex]2x-1 = -2\\2x = -2 + 1 \\2x = -1\\x = -\frac{1}{2}[/tex]
