1a) \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)

=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}=4x-1\\\frac{3}{2}x+\frac{1}{2}=1-4x\end{cases}}\)

=> \(\orbr{\begin{cases}-\frac{5}{2}x=-\frac{3}{2}\\\frac{11}{2}x=\frac{1}{2}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{5}{3}\\x=\frac{1}{11}\end{cases}}\)

b) \(\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)

=>\(\left|\frac{5}{4}x-\frac{7}{2}\right|=\left|\frac{5}{8}x+\frac{3}{5}\right|\)

=> \(\orbr{\begin{cases}\frac{5}{4}x-\frac{7}{2}=\frac{5}{8}x+\frac{3}{5}\\\frac{5}{4}x-\frac{7}{2}=-\frac{5}{8}x-\frac{3}{5}\end{cases}}\)

=> \(\orbr{\begin{cases}\frac{5}{8}x=\frac{41}{10}\\\frac{15}{8}x=\frac{29}{10}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)

c) TT

a, \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\)

=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}=4x-1\\-\frac{3}{2}x-\frac{1}{2}=4x-1\end{cases}}\)

=> \(\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}-4x=-1\\-\frac{3}{2}x-\frac{1}{2}-4x=-1\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{3}{5}\\x=\frac{1}{11}\end{cases}}\)

\(b,\left|\frac{5}{4}x-\frac{7}{2}\right|-\left|\frac{5}{8}x+\frac{3}{5}\right|=0\)

=> \(\left|\frac{5}{4}x-\frac{7}{2}\right|-0=\left|\frac{5}{8}x+\frac{3}{5}\right|\)

=> \(\frac{\left|5x-14\right|}{4}=\frac{\left|25x+24\right|}{40}\)

=> \(\frac{10(\left|5x-14\right|)}{40}=\frac{\left|25x+24\right|}{40}\)

=> \(\left|50x-140\right|=\left|25x+24\right|\)

=> \(\orbr{\begin{cases}50x-140=25x+24\\-50x+140=25x+24\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{164}{25}\\x=\frac{116}{75}\end{cases}}\)

c, \(\left|\frac{7}{5}x+\frac{2}{3}\right|=\left|\frac{4}{3}x-\frac{1}{4}\right|\)

=> \(\orbr{\begin{cases}\frac{7}{5}x+\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\\-\frac{7}{5}x-\frac{2}{3}=\frac{4}{3}x-\frac{1}{4}\end{cases}}\)

=> \(\orbr{\begin{cases}x=-\frac{55}{4}\\x=-\frac{25}{164}\end{cases}}\)

Bài 2 : a. |2x - 5| = x + 1

 TH1 : 2x - 5 = x + 1

    => 2x - 5 - x = 1

    => 2x - x - 5 = 1

    => 2x - x = 6

    => x = 6

TH2 : -2x + 5 = x + 1

   => -2x + 5 - x = 1

   => -2x - x + 5 = 1

   => -3x = -4

   => x = 4/3

Ba bài còn lại tương tự

Câu d:

-1\(\frac23\) - (|2\(x\)| + \(\frac56\)) = - 2

-\(\frac53\) - |2\(x\)| - \(\frac56\) = - 2

|2\(x\)| = - \(\frac53\) - \(\frac56\) + 2

|2\(x\)| = - \(\frac52\) + 2

|2\(x\)| = - \(\frac12\) (vô lí vì trị tuyệt đối của một số luôn là một số không âm)

Không có giá trị nào của x thỏa mãn đề bài.

x ∈ ∅

Câu a:

|\(x\) - 3| = \(x\) + 4

Vì |\(x\) - 3| ≥ 0 ∀ \(x\) nên \(x\) + 4 ≥ 0 ⇒ \(x\) ≥ - 4

Với -4 ≤ \(x\) ≤ 3 ta có:

-\(x\) + 3 = \(x\) + 4

\(x\) + \(x\) = -4 + 3

2\(x\) = -1

\(x=\frac{-1}{2}\)

Với x > 3 ta có:

x - 3 = x + 4

x - x = 3 + 4

0 = 7 (vô lí)

Vậy x = -1/2 là nghiện duy nhất của phương trình.

Vậy \(x\) = -1/2

a) \(\left|0,5x-2\right|-\left|x+\frac{1}{3}\right|=0\)

=> \(\left|0,5x-2\right|=\left|x+\frac{1}{3}\right|\)

=> \(\orbr{\begin{cases}0,5x-2=x+\frac{1}{3}\\0,5x-2=-x-\frac{1}{3}\end{cases}}\)

=> \(\orbr{\begin{cases}-0,5x=\frac{7}{3}\\1,5x=\frac{5}{3}\end{cases}}\)

=> \(\orbr{\begin{cases}x=-\frac{14}{3}\\x=\frac{10}{9}\end{cases}}\)

b) \(2x-\left|x+1\right|=\frac{1}{2}\)

=> \(\left|x+1\right|=2x-\frac{1}{2}\) (Đk: \(2x-\frac{1}{2}\ge0\) <=> \(x\ge\frac{1}{4}\))

=> \(\orbr{\begin{cases}x+1=2x-\frac{1}{2}\\x+1=\frac{1}{2}-2x\end{cases}}\)

=> \(\orbr{\begin{cases}-x=-\frac{3}{2}\\3x=-\frac{1}{2}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{3}{2}\\x=-\frac{1}{6}\end{cases}}\)

Câu c:

|2x -1| - |x + 1/3| = 0

|2x -1| = |x + 1/3|

2x - 1 = x + 1/3 hoặc 2x - 1 = - x + 1/3

2x - x = 1/3 + 1

x = 4/3

2x - 1 = - x + 1/3

2x + x = 1/3 + 1

3x = 4/3

x = 4/3 : 3

x = 4/9

Vậy x ∈ {4/9; 4/3}

(2x-3)( 3/4x+1) = 0

=> 2x-3= 0 hoặc 3/4x +1 = 0

=> 2x= 3 hoặc 3/4x = -1

=> x=3/2 hoặc x= -4/3

(5x-1)(2x-1/3) = 0

=> 5x-1 = 0 hoặc 2x-1/3 = 0

5x =1 hoặc 2x=1/3

x=1/5 hoặc x= 1/6

x=1/5 hoac x=1/6

\(\left|\left(x+\frac{1}{2}\right).\left|2x-\frac{3}{4}\right|\right|=2x-\frac{3}{4}\)

\(\Rightarrow\left|x+\frac{1}{2}\right|.\left|2x-\frac{3}{4}\right|=2x-\frac{3}{4}\)

\(\Rightarrow2x-\frac{3}{4}\ge0\) (1)

Lúc này ta có: \(\left|x+\frac{1}{2}\right|.\left(2x-\frac{3}{4}\right)=2x-\frac{3}{4}\)

\(\Rightarrow\left|x+\frac{1}{2}\right|.\left(2x-\frac{3}{4}\right)-\left(2x-\frac{3}{4}\right)=0\)

\(\Rightarrow\left(2x-\frac{3}{4}\right).\left(\left|x+\frac{1}{2}\right|-1\right)=0\)

\(\Rightarrow\left[\begin{array}{nghiempt}2x-\frac{3}{4}=0\\\left|x+\frac{1}{2}\right|-1=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}2x=\frac{3}{4}\\\left|x+\frac{1}{2}\right|=1\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{3}{8}\\x+\frac{1}{2}=1\\x+\frac{1}{2}=-1\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{3}{8}\\x=\frac{1}{2}\\x=\frac{-3}{2}\end{array}\right.\)

Mà \(x\ge\frac{3}{8}\) do \(2x-\frac{3}{4}\ge0\)

Vậy \(x\in\left\{\frac{3}{8};\frac{1}{2}\right\}\)

\(\left(2x+\frac{1}{2}\right).\left(\frac{3}{4}-x\right)=0\)

• \(2x+\frac{1}{2}=0\)

                    \(2x=-\frac{1}{2}\)

                      \(x=-\frac{1}{2}\div2\)

                      \(x=-\frac{1}{2}\times\frac{1}{2}\)

                      \(x=-\frac{1}{4}\)

•  \(\frac{3}{4}-x=0\)​

                    \(x=\frac{3}{4}\) 

Vậy  \(x=-\frac{1}{4}\) hoặc \(x=\frac{3}{4}\)

ta co 2 truong hop

th1: 2x+1/2=0=>2x=0+1/2=>2x=1/2=>x=1/2:2=>x=1/4

th2: 3/4-x=0=>x=3/4-0=>x=3/4

x=4,y=6

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