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Ta có : \(156:\left(7x+135\right):x=\frac{156}{\frac{7x+135}{x}}=156.\frac{x}{7x+135}\)
\(\Rightarrow156.\frac{x}{7x+135}=13\)
\(\Rightarrow\frac{x}{7x+135}=\frac{13}{156}\)
\(\Rightarrow\frac{x}{7x+135}=\frac{1}{12}\)
\(\Rightarrow12x=7x+135\)
\(\Rightarrow5x=135\)
\(\Rightarrow x=27\)
\(156:\left(7x+135\right):x=13\)
\(\left(7x+135\right):x=12\)
\(7x+135=12x\)
\(7x-12x=-135\)
\(-5x=-135\)
\(x=\frac{-135}{-5}\)
\(x=27\)
hok tốt!!
Bài 6:
\(\Leftrightarrow6n+4⋮2n-1\)
\(\Leftrightarrow2n-1\in\left\{1;-1;7;-7\right\}\)
hay \(n\in\left\{1;0;4;-3\right\}\)
\(\dfrac{3}{5}x-\dfrac{1}{2}x=\dfrac{3}{2}-0\)
\(\left(\dfrac{3}{5}-\dfrac{1}{2}\right)x=\dfrac{3}{2}\)
\(\dfrac{1}{10}\cdot x=\dfrac{3}{2}\)
\(x=\dfrac{3}{2}:\dfrac{1}{10}\)
\(x=15\)
\(\dfrac{3}{5x}-\dfrac{1}{2x}=\dfrac{3}{2-0}\)
\(\dfrac{3}{5x}+\dfrac{-1}{2x}=\dfrac{3}{2}\)
\(\dfrac{3}{5}+\dfrac{-1}{2}=\dfrac{3}{2}\cdot x\)
\(\dfrac{1}{10}=\dfrac{3}{2}\cdot x\)
\(\dfrac{3}{2}\cdot x=\dfrac{1}{10}\)
\(x=\dfrac{1}{10}\div\dfrac{3}{2}\)
\(x=\dfrac{2}{30}\)
\(x=\dfrac{1}{15}\)
Do ƯCLN(a; b) = 5 nên đặt a = 5x; b = 5y (x và y nguyên tố cùng nhau)
Do a + b = 300
⇒ 5x + 5y = 300
⇒ 5(x + y) = 300
⇒ x + y = 60
⇒ (x; y) ∈ {(1; 59); (7; 53); (11;49); (13; 47); (17; 43); (19; 41); (23; 37); (29; 31); (31; 29); (37; 23); (41; 19); (43; 17); (47; 13); (49; 11); (53; 7); (59; 1)}
⇒ (a; b) ∈ {(5; 295); (35; 265); (55; 245); (65; 235); (85; 215); (95; 205); (115; 185); (145; 155); (155; 145); (185; 115); (205; 95); (215; 85); (235; 65); (245; 55); (265; 35); (295; 5)}
e) \(20\%\cdot1\dfrac{1}{4}\cdot12\cdot\dfrac{25}{45}\cdot0,6\)
\(=\dfrac{1}{5}\cdot\dfrac{5}{4}\cdot\dfrac{12}{1}\cdot\dfrac{5}{9}\cdot\dfrac{6}{10}\)
\(=1\)