a, <=> 6x-3-5x-5-4.5=0

<=> x=28

b, 5|3x+1|-4|3x+1|=19

<=> |3x+1|=19

<=>\(\orbr{\begin{cases}3x+1=19\\3x+1=-19\end{cases}}\)

<=>\(\orbr{\begin{cases}x=6\\x=\frac{-20}{3}\end{cases}}\)

Chúc hok tốt!!

Do |3x-5| lớn hơn hoặc bằng 0; |2/3x+1/2| lớn hơn hoặc bằng 0

=> |3x-5|+|2/3x+1/2| lớn hơn hoặc bằng 0

Dấu bằng xảy ra khi 3x-5=0 đồng thời 2/3x+1/2=0

Không có GT nào t/m

\(1,|5x|=x-12\)

\(\Rightarrow\orbr{\begin{cases}5x=x-12\\5x=12-x\end{cases}\Rightarrow}\orbr{\begin{cases}4x=-12\\6x=12\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=2\end{cases}}}\)

\(2,|7-x|=5x+1\)

\(\Rightarrow\orbr{\begin{cases}7-x=5x+1\\7-x=-5x-1\end{cases}\Rightarrow}\orbr{\begin{cases}6x=6\\4x=-8\end{cases}\Rightarrow}\orbr{\begin{cases}x=1\\x=-2\end{cases}}\)

\(3,|2x-3|+x=21\)

\(\Rightarrow|2x-3|=21-x\)

\(\Rightarrow\orbr{\begin{cases}2x-3=21-x\\2x-3=x-21\end{cases}\Rightarrow}\orbr{\begin{cases}3x=24\\x=-18\end{cases}\Rightarrow}\orbr{\begin{cases}x=8\\x=-18\end{cases}}\)

\(4,|4+2x|=-4x\)

\(\Rightarrow\orbr{\begin{cases}4+2x=4x\\4+2x=-4x\end{cases}\Rightarrow}\orbr{\begin{cases}2x=4\\-6x=4\end{cases}\Rightarrow}\orbr{\begin{cases}x=2\\x=-\frac{2}{3}\end{cases}}\)

\(5,|3x-1|+2=x\)

\(\Rightarrow|3x-1|=x-2\)

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

\(6,|2x-5|+x=2\)

\(\Rightarrow|2x-5|=2-x\)

\(\Rightarrow\orbr{\begin{cases}2x-5=2-x\\2x-5=x-2\end{cases}\Rightarrow\orbr{\begin{cases}3x=7\\x=3\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{7}{3}\\x=3\end{cases}}}\)

\(7,|2x-5|=x+1\)

\(\Leftrightarrow\orbr{\begin{cases}2x-5=x+1\\2x-5=-x-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-x=1+5\\2x+x=-1+5\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=6\\3x=4\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=6\\x=\frac{4}{3}\end{cases}}\)

\(8,|3x-2|-1=x\)

\(\Leftrightarrow|3x-2|=x+1\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}2x=3\\4x=1\end{cases}}\)

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

-|3x - 7| - |y + 5| - 1 = 0
<=> - 1 = |3x - 7| + |y + 5| (*)
Ta có: VP=|3x - 7| + |y + 5|≥0 với mọi x;y
VT=-1<0
Nên pt (*) vô nghiệm
Vậy pt đã cho vô nghiệm.

\(a)\left|2x-5\right|=4\)\(\Rightarrow2x-5=\pm4\)

\(Với\)\(2x-5=4\Rightarrow2x=9\Rightarrow x=\frac{9}{2}\)

\(Với\)\(2x-5=-4\Rightarrow2x=1\Rightarrow x=\frac{1}{2}\)

\(Vậy\)\(x=\frac{9}{2};x=\frac{1}{2}\)

\(b)\left|2x-3\right|-\left|3x+2\right|=0\)

\(Vì\)\(\left|2x-3\right|\ge0;\left|3x+2\right|\ge0\)

\(\Rightarrow\hept{\begin{cases}2x-3=0\\3x+2=0\end{cases}\Rightarrow\hept{\begin{cases}2x=3\\3x=-2\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{3}{2}\\x=\frac{-2}{3}\end{cases}}}\)

\(Vậy\)\(x=\frac{3}{2};x=\frac{-2}{3}\)

a) |3x-2| + 5x = 4x - 10 

<=> |3x-2| = -x - 10

Ta có |3x-2| = 3x-2 nếu x>=2/3 ; = -3x + 2 nếu x<2/3

+TH1: 3x-2 = -x - 10 

<=> x = -2 (loại vì x < 2/3)

+TH2: -3x + 2 = -x - 10

<=> x = 6 (loại vì x > 2/3)

Vậy không có x thoả mãn

b) 3 + |2x+5| > 13

<=> |2x+5| > 10

Gợi ý: Xét 2TH: 2x + 5 > 10 và 2x + 5< -10 rồi tìm ra x

\(\left|2x-1\right|=\left|3x+5\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=3x+5\\2x-1=-3x-5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=-\dfrac{4}{5}\end{matrix}\right.\)