Toán Lớp 7: tìm x,y biết : |x+1|+|x+2|+|x+3|=x. b: |2x+1+|x-y+1|=0. c: |x-3|+3=x

Question

Toán Lớp 7:  tìm x,y biết : |x+1|+|x+2|+|x+3|=x. b: |2x+1+|x-y+1|=0. c: |x-3|+3=x

bichquyenlien · Answer

$a$) $|x+1| + |x+2| + |x+3| = x$   V&igrave; $|x+1| ; |x+2| ; |x+3| &ge; 0 &forall;$ $x$    $&rArr;$ $|x+1| + |x+2| + |x+3| = x &ge; 0$   $&rArr;$ $|x+1| + |x+2| + |x+3| = (x+1)+(x+2)+(x+3) = x$   $&hArr; 3x + 6 = x$   $&hArr; 3x+6-x=0$   $&hArr; 2x = -6$   $&hArr; x = -3$      Vậy $x=-3$.   $b$) $|2x+1|+|x-y+1|=0$    V&igrave; $|2x+1|;|x-y+1|&ge; 0 &forall;$ $x;y$      $&rArr;$ $|2x+1|+|x-y+1|=0$ $&hArr;$ $2x+1 = x-y+1 = 0$     $&rArr;$ $x= dfrac{-1}{2}$     $&rArr;  dfrac{-1}{2} - y + 1 = 0$     $&rArr; y =  dfrac{1}{2}$        Vậy (x;y)=(-1/2;1/2).     $c$) $|x-3| + 3 = x$  ($1$)     $&hArr; |x-3| = x-3$     Nếu $x -3 &ge; 0 &rArr; x &ge; 3$     Khi đ&oacute; ($1$) trở th&agrave;nh : $x-3 = x-3$     $&rArr; x &ge; 3$   ($*$)     Nếu  $x -3 &le; 0 &rArr; x &le; 3$    Khi đ&oacute; ($1$) trở th&agrave;nh : $3-x= x-3$     $&hArr; 3-x+x = x-3+x$     $&hArr; 2x-3 = 3$     $&hArr; x=3$  ($**$)     Từ $(*);(**)$ $&rArr;$ $x &ge; 3$         Vậy $x &ge; 3$.