\(\Leftrightarrow\)\(\dfrac{7x-1}{6}+2x=\dfrac{14}{5}\)
\(\Leftrightarrow\)\(\dfrac{7x-1}{6}+\dfrac{12x}{6}=\dfrac{14}{5}\)
\(\Leftrightarrow\)\(\dfrac{7x-1+12x}{6}=\dfrac{14}{5}\)
\(\Leftrightarrow\)\(\dfrac{19x-1}{6}=\dfrac{14}{5}\)
\(\Rightarrow\)\(5(19x-1)=6.14\)
\(\Leftrightarrow\)\(95x-5=84\)
\(\Leftrightarrow\)\(x=\dfrac{89}{95}\)
a) 5 - (x - 6) = 4(3 - 2x)
\(\Leftrightarrow\) 5 - x + 6 = 12 - 4x
\(\Leftrightarrow\) 5 - x + 6 - 12 + 4x = 0
\(\Leftrightarrow\) -1 + 3x = 0
\(\Leftrightarrow\) 3x = 1
\(\Leftrightarrow\) x = \(\dfrac{1}{3}\)
Vậy S = \(\left\{\dfrac{1}{3}\right\}\)
b) 2x(x + 2)2 - 8x2 = 2(x - 2)(x2 + 2x + 4)
\(\Leftrightarrow\) 2x(x2 + 4x + 4) - 8x2 = 2(x3 - 8)
\(\Leftrightarrow\) 2x3 + 8x2 + 8x - 8x2 = 2x3 - 16
\(\Leftrightarrow\) 2x3 + 8x2 + 8x - 8x2 - 2x3 + 16 = 0
\(\Leftrightarrow\) 8x + 16 = 0
\(\Leftrightarrow\) 8x = -16
\(\Leftrightarrow\) x = \(\dfrac{-16}{8}=-2\)
Vậy S = \(\left\{-2\right\}\)
c) 7 - (2x + 4) = -(x + 4)
\(\Leftrightarrow\) 7 - 2x - 4 = -x - 4
\(\Leftrightarrow\) 7 - 2x - 4 + x + 4 = 0
\(\Leftrightarrow\) 7 - x = 0
\(\Leftrightarrow\) x = 7
Vậy S = \(\left\{7\right\}\)
d) (x + 1)(2x - 3) = (2x - 1)(x + 5)
\(\Leftrightarrow\) 2x2 - x - 3 = 2x2 - 9x - 5
\(\Leftrightarrow\) 2x2 - x - 3 - 2x2 + 9x + 5 = 0
\(\Leftrightarrow\) 8x + 2 = 0
\(\Leftrightarrow\) 8x = 2
\(\Leftrightarrow\) x = \(\dfrac{2}{8}=\dfrac{1}{4}\)
Vậy S = \(\left\{\dfrac{1}{4}\right\}\)
e) \(\dfrac{\left(2x+1\right)^2}{5}-\dfrac{\left(x-1\right)^2}{3}=\dfrac{7x^2-14x-5}{15}\)
MTC : `15
Quy đồng mẫu thức :
\(\Rightarrow\) \(\dfrac{3\left(2x+1\right)^2}{15}-\dfrac{5\left(x-1\right)^2}{15}=\dfrac{7x^2-14x-5}{15}\)
Suy ra : 3(2x + 1)2 - 5(x - 1)2 = 7x2 - 14x - 5
\(\Leftrightarrow\) 3(4x2 + 4x + 1) - 5(x2 - 2x + 1) = 7x2 - 14x - 5
\(\Leftrightarrow\) 12x2 + 12x + 3 - 5x2 + 10x - 5 - 7x2 + 14x + 5 = 0
\(\Leftrightarrow\) 36x + 3 = 0
\(\Leftrightarrow\) 36x = -3
\(\Leftrightarrow\) x = \(\dfrac{-3}{36}=-\dfrac{1}{12}\)
Vậy S = \(\left\{-\dfrac{1}{12}\right\}\)
f) \(\dfrac{7x-1}{6}-2x=\dfrac{16-x}{5}\)
MTC : 30
Quy đồng mẫu thức :
⇒ \(\dfrac{5\left(7x-1\right)}{30}+\dfrac{60x}{30}=\dfrac{6\left(16-x\right)}{30}\)
Suy ra : 5(7x - 1) + 60x = 6(16 - x)
\(\Leftrightarrow\) 35x - 5 + 60x = 96 - 6x
\(\Leftrightarrow\) 35x - 5 + 60x - 96 + 6x = 0
\(\Leftrightarrow\) 101x - 101 = 0
\(\Leftrightarrow\) 101x = 101
\(\Leftrightarrow\) x = \(\dfrac{101}{101}=1\)
Vậy S = \(\left\{1\right\}\)
Chúc bạn học tốt
Mình xin lỗi bạn nhé , taih hồi nãy minh thấy bạn đăng nhiều bài nên ngồi làm , giờ thấy bạn đăng lại nên mình làm lại :
\(\dfrac{7x-1}{6}+2x=\dfrac{14}{5}\)
MTC : 30
Quy đồng mẫu thức :
⇒ \(\dfrac{5\left(7x-30\right)}{30}+\dfrac{60x}{30}=\dfrac{84}{30}\)
Suy ra: 5(7x - 30) + 60x = 84
\(\Leftrightarrow\) 35x - 150 + 60x - 84 = 0
\(\Leftrightarrow\) 95x - 234 = 0
\(\Leftrightarrow\) 95x = 234
\(\Leftrightarrow\) x = \(\dfrac{234}{95}\)
Vậy S = \(\left\{\dfrac{234}{95}\right\}\)
Chúc bạn học tốt