tìm x biết
\(3\frac{x}{5}=\frac{3x+7}{5}\)
giải cả bài nha
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3 /x/5 = (3.x+7)/5
=>( 3.5 +x )/ 5= 3.x +7/5
=>(15+x) /5=(3.x+7)/5
=>(15-7+x)/5 =(3.x)/5
=>8+x=3.x
=>8=3.x-x
=>8=2.x
=>x=8:2
=. x= 4
\(\Leftrightarrow\dfrac{x+15}{5}=\dfrac{3x+7}{5}\)
=>3x+7=x+15
=>2x=8
hay x=4
3\(\frac{x}{5}\) = \(\frac{3x+7}{5}\)
Mà 3\(\frac{x}{5}\) =\(\frac{15+x}{5}\)
Suy ra: \(\frac{15+x}{5}\) =\(\frac{3x+7}{5}\)
15+x=3x+7
15+x-7=3x+7-7
8+x=3x
Suy ra: 8=2x
x=8:2
x=4
Suy ra:(3x-5)*3=4x*2
9x-15=8x
15=9x-8x
15=x
Vậy x=15(tick nha)
\(\frac{3.\left(3x-5\right)}{6}=\frac{2.\left(4x\right)}{6}\)
\(3.\left(3x-5\right)=2.4x\)
\(9x-15=8x\)
\(9x-8x=15\)
\(x=15\)
\(\frac{3x-5}{2}=\frac{4x}{3}\Rightarrow3.\left(3x-5\right)=2.4x\Rightarrow9x-15=8x\Rightarrow9x-8x=15\Rightarrow x=15\)
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
=> \(\frac{3.5+x}{5}=\frac{3x+7}{5}\Rightarrow3.5+x=3x+7\)
=> 3.5 = 2x + 7
=> 2x = 15 - 7 = 8
=> x = 8 : 2 = 4
Vậy x = 4