Toán Lớp 7: a |x-1|-2x=1/2 b 3x-|x+15|= 5/4

Question

Toán Lớp 7:  a |x-1|-2x=1/2 b 3x-|x+15|= 5/4

khanhlanchau · Answer

$  $   a,   |x-1| - 2x=1/2   -> |x-1| = 1/2 + 2x (1)   Điều kiện : 1/2 + 2x &ge; 0 -> 2x &ge; (-1)/2 -> x &ge; (-1)/4   Khi đ&oacute; (1) c&oacute; dạng :   -> |x-1| = |2x + 1/2|   ->  ( left[  begin{array}{l}x-1=2x+ dfrac{1}{2}  x-1=-2x- dfrac{1}{2} end{array}  right. ) $  $ ->  ( left[  begin{array}{l}x-2x=1+ dfrac{1}{2}  x+2x=1- dfrac{1}{2} end{array}  right. ) $  $ ->  ( left[  begin{array}{l}-x= dfrac{3}{2}   3x= dfrac{1}{2}  end{array}  right. ) $  $ ->  ( left[  begin{array}{l}x= dfrac{-3}{2}  text{(Kh&ocirc;ng thỏa m&atilde;n)}  x= dfrac{1}{6} text{(Thỏa m&atilde;n)} end{array}  right. )    Vậy x=1/6   $  $   b,   3x - |x+15|=5/4   -> |x+15|=3x-5/4 (1)   Điều kiện : 3x-5/4 &ge; 0 -> 3x &ge; 5/4 -> x&ge;5/12   Khi đ&oacute; (1) c&oacute; dạng :   -> |x+15|=|3x-5/4|   ->  ( left[  begin{array}{l}x+15=3x- dfrac{5}{4}  3x+15=-3x+ dfrac{5}{4} end{array}  right. ) $  $ ->  ( left[  begin{array}{l}x-3x=-15- dfrac{5}{4}  x+3x=-15+ dfrac{5}{4} end{array}  right. ) $  $ ->  ( left[  begin{array}{l}-2x= dfrac{-65}{4}  4x= dfrac{-55}{4} end{array}  right. ) $  $ ->  ( left[  begin{array}{l}x= dfrac{65}{8} text{(Thỏa m&atilde;n)}  x= dfrac{-55}{16}  text{(Kh&ocirc;ng thỏa m&atilde;n)} end{array}  right. )    Vậy x=65/8

aivilanlan · Answer

Giải đáp + Lời giải và giải thích chi tiết:     a)   ĐKXĐ : x < 1 , x  ge 1   |x-1| - 2x = 1/2    to |x-1| = 1/2 + 2x   TH1 : ĐK : x  ge 1   x - 1 = 1/2 + 2x    to x - 2x = 1 + 1/2    to -x = 3/2    to x = -3/2 (Kh&ocirc;ng thỏa m&atilde;n)   TH2 : ĐK : x < 1   -(x-1) = 1/2 + 2x    to -x + 1 = 1/2 + 2x    to -x - 2x = 1/2 - 1    to -3x = -1/2    to x = 1/6 (Thỏa m&atilde;n)   Vậy x  in {1/6}   b)   ĐKXĐ : x < -15 , x  ge -15   3x - |x+15| = 5/4    to |x+15| = 3x - 5/4   TH1 : ĐK : x  ge -15   x+15 = 3x - 5/4    to 3x-x = 15+5/4    to 2x = 65/4    to x = 65/8 (Thỏa m&atilde;n)   TH2 : ĐK : x < -15   -(x+15) = 3x - 5/4    to -x - 15 = 3x - 5/4    to -x - 3x = 15 - 5/4    to -4x = 55/4    to x = -55/16 (Kh&ocirc;ng thỏa m&atilde;n)   Vậy x  in {65/18}