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a: \(\Leftrightarrow\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+....+\dfrac{1}{9}-\dfrac{1}{10}\right)\cdot\left(x-1\right)+\dfrac{1}{10}x-x=-\dfrac{9}{10}\)
\(\Leftrightarrow\dfrac{9}{10}x-\dfrac{9}{10}-\dfrac{9}{10}x=-\dfrac{9}{10}\)
=>-9/10=-9/10(luôn đúng)
b: \(\Leftrightarrow\dfrac{195x+195+130x+195+117x+195+100x+195}{195}=\dfrac{22\cdot39+4\cdot65+6\cdot39+40\cdot5}{195}\)
=>347x+780=1552
=>347x=772
hay x=772/347
\(\frac{x-3}{5}-\frac{2x-1}{10}=\frac{x+1}{2}+\frac{1}{4}\)
\(< =>\frac{\left(x-3\right).4}{20}-\frac{\left(2x-1\right).2}{20}=\frac{\left(x+1\right).10}{20}+\frac{5}{20}\)
\(< =>4x-12-4x+2=10x+10+5\)
\(< =>10x=-10-10-5=-25\)
\(< =>x=-\frac{25}{10}=-\frac{5}{2}\)
\(\frac{x+3}{2}-\frac{2x-1}{3}-1=\frac{x+5}{5}\)
\(< =>\frac{\left(x+3\right).15}{30}-\frac{\left(2x-1\right).10}{30}-\frac{30}{30}=\frac{\left(x+5\right).5}{30}\)\(< =>15x+45-20x+10-30=5x+25\)
\(< =>-5x+25=5x+25< =>10x=0< =>x=0\)
<=>\(\left(\frac{x}{1}+\frac{2x}{3}+\frac{3x}{5}+...+\frac{20x}{39}\right)+\left(\frac{1}{1}+\frac{3}{3}+\frac{5}{5}+...+\frac{39}{39}\right)=20+2.\left(\frac{1}{1}+\frac{2}{3}+\frac{3}{5}+...+\frac{20}{39}\right)\)<=>
\(\left(\frac{1}{1}+\frac{2}{3}+\frac{3}{5}+...+\frac{20}{39}\right).x+20=20+2.\left(\frac{1}{1}+\frac{2}{3}+\frac{3}{5}+...+\frac{20}{39}\right)\)
<=> \(\left(\frac{1}{1}+\frac{2}{3}+\frac{3}{5}+...+\frac{20}{39}\right).x=2.\left(\frac{1}{1}+\frac{2}{3}+\frac{3}{5}+...+\frac{20}{39}\right)\)<=> x = 2
(x+1) / 1 + (2x+3) / 3 + (3x+5) / 5+ ... + (20x + 39) / 39
= 22 + 4 /3 + 6 / 5 +... + 40 /39
<=> x+ 1+ 2x / 3 +1 + 3x / 5+1+...+20x / 39+1 = 22+4 / 3+6 / 5+8 / 7+...+38 / 37+40 / 39
<=> (1+2 / 3+3 / 5+4 / 7+...+19 / 37+20 / 39)x + 20 = 22+4/3+6/5+8/7+...+38/37+40/39
<=> (1+2/3+3/5+4/7+...+19/37+20/39)x = 2(1 + 2/3 + 3/5 + 4/7 +...+ 19/37 + 20/39)
<=> x = 2
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{9.10}\right)\left(x-1\right)+\frac{1}{10}x=x-\frac{9}{10}\)
\(\Rightarrow\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{9}-\frac{1}{10}\right)\left(x-1\right)+\frac{1}{10}x=x-\frac{9}{10}\)
\(\Rightarrow\left(1-\frac{1}{10}\right)\left(x-1\right)+\frac{1}{10}x=x-\frac{9}{10}\)
\(\Rightarrow\frac{9}{10}.\left(x-1\right)+\frac{1}{10}x=x-\frac{9}{10}\)
\(\Rightarrow\frac{9}{10}x-\frac{9}{10}+\frac{1}{10}x=x-\frac{9}{10}\)
\(\Rightarrow\left(\frac{9}{10}x+\frac{1}{10}x\right)-\frac{9}{10}=x-\frac{9}{10}\)
\(\Rightarrow x-\frac{9}{10}=x-\frac{9}{10}\)
\(\Rightarrow x\inℝ\)
Vậy \(x\inℝ\)
a) \(\frac{7x}{8}-5\left(x-9\right)=\frac{20x+1,5}{6}\)
\(\Leftrightarrow\frac{7x}{8}-\frac{40\left(x-9\right)}{8}=\frac{20x+1,5}{6}\)
\(\Leftrightarrow\frac{7x}{8}-\frac{40x-360}{8}=\frac{20x+1,5}{6}\)
\(\Leftrightarrow\frac{360-33x}{8}=\frac{20x+1,5}{6}\)
\(\Leftrightarrow2160-198x=160x+12\)
\(\Leftrightarrow358x=2148\)
\(\Leftrightarrow x=6\)
Vậy nghiệm của pt x=6
b) \(\frac{5\left(x-1\right)+2}{6}-\frac{7x-1}{4}=\frac{2\left(2x+1\right)}{7}-5\)
\(\Leftrightarrow\frac{10\left(x-1\right)+4}{12}-\frac{21x-3}{12}=\frac{4x+2}{7}-\frac{35}{7}\)
\(\Leftrightarrow\frac{-11x-3}{12}=\frac{4x-33}{7}\)
\(\Leftrightarrow-77x-21=48x-396\)
\(\Leftrightarrow125x=375\)
\(\Leftrightarrow3\)
Vậy nghiệm của pt x=3
hghhhhhhg
nhìn lại đề bài phần a) đi