Toán Lớp 7: TÌm x, biết: a, ||x-1/4|-3/2|=1/4 b, ||1/2x+1|-1/4|=3/2

Question

Toán Lớp 7:  TÌm x, biết: a, ||x-1/4|-3/2|=1/4 b, ||1/2x+1|-1/4|=3/2

lantrungbach · Answer

Giải đáp: + Lời giải và giải thích chi tiết:   $a$) ||x-1/4|-3/2| = 1/4   $&rArr;$  ( left[  begin{array}{l}|x- dfrac{1}{4}|= dfrac{1}{4}+ dfrac{3}{2}  |x- dfrac{1}{4}|=- dfrac{1}{4}+ dfrac{3}{2} end{array}  right. )    $&hArr;$  ( left[  begin{array}{l}|x- dfrac{1}{4}|= dfrac{7}{4}  |x- dfrac{1}{4}|= dfrac{5}{4} end{array}  right. )    $&hArr;$  ( left[  begin{array}{l}x= dfrac{7}{4}+ dfrac{1}{4}  x=- dfrac{7}{4}+ dfrac{1}{4}  x= dfrac{5}{4}+ dfrac{1}{4}   x=- dfrac{5}{4} +  dfrac{1}{4} end{array}  right. )   $&hArr;$  ( left[  begin{array}{l}x=2  x=- dfrac{3}{2}  x= dfrac{3}{2}   x=-1 end{array}  right. )      Vậy $x$ $&isin;$ {-1; &plusmn; 3/2 ; 2}.   $b$) ||1/2 x+1|-1/4| = 3/2   $&rArr;$  ( left[  begin{array}{l}| dfrac{1}{2} x+1|= dfrac{3}{2}+ dfrac{1}{4}  | dfrac{1}{2}x+1|=- dfrac{3}{2}+ dfrac{1}{4} end{array}  right. )    $&hArr;$  ( left[  begin{array}{l}| dfrac{x}{2} + 1|= dfrac{7}{4}  | dfrac{x}{2} + 1|=- dfrac{5}{4}(KTM) end{array}  right. )    $&hArr;$  ( left[  begin{array}{l} dfrac{x}{2} =  dfrac{7}{4} - 1   dfrac{x}{2} =  dfrac{-7}{4}-1 end{array}  right. )    $&hArr;$  ( left[  begin{array}{l} dfrac{x}{2} = dfrac{3}{4}   dfrac{x}{2} =  dfrac{-11}{4} end{array}  right. )    $&hArr;$  ( left[  begin{array}{l}x= dfrac{3}{2}  x= dfrac{-11}{2} end{array}  right. )      Vậy $x$ $&isin;$ {-{11}/2 ; 3/2}.