I : Phan trac nghiem :
Cau 1 : B
Cau 2 : C
Cau 3 : A
Cau 4 : D
II Phan tu luan :
Cau 1 :
a) 2x - 3 = 0
\(\Leftrightarrow\) 2x = 3
\(\Leftrightarrow\) x = \(\dfrac{3}{2}\)
Vay S = \(\left\{\dfrac{3}{2}\right\}\)
c) \(\dfrac{1}{x-1}-\dfrac{3}{x-2}=\dfrac{-1}{\left(x-1\right)\left(x-2\right)}\)
dkxd : x ≠ 1
x ≠ 2
MTC : (x - 1)(x - 2)
\(\Rightarrow\) \(\dfrac{1\left(x-2\right)}{\left(x-1\right)\left(x-2\right)}\) - \(\dfrac{3\left(x-1\right)}{\left(x-1\right)\left(x-2\right)}=\dfrac{-1}{\left(x-1\right)\left(x-2\right)}\)
Suy ra : 1(x - 2) - 3(x - 1) = -1
\(\Leftrightarrow\) x - 2 - 3x + 3 + 1 = 0
\(\Leftrightarrow\) -2x + 2 = 0
\(\Leftrightarrow\) -2x = -2
\(\Leftrightarrow\) x = \(\dfrac{-2}{-2}=1\) (khong thoa man)
Vay S = \(\varnothing\)
b) \(\dfrac{x+3}{5}< \dfrac{5-x}{3}\)
MTC : 15
\(\Rightarrow\dfrac{3\left(x+3\right)}{15}< \dfrac{5\left(5-x\right)}{15}\)
Suy ra : 3(x + 3) < 5(5 - x)
\(\Leftrightarrow\) 3x + 9 < 25 - 5x
\(\Leftrightarrow\) 3x + 5x < 25 - 9
\(\Leftrightarrow\) 8x < 16
\(\Leftrightarrow\) x < \(\dfrac{16}{8}=2\)
\(\Leftrightarrow\) x < 2
Vay x < 2
Cau 2 : 20 phut : \(\dfrac{1}{3}\) gio
Goi x la quang duong AB ( x : km)
Thoi gian xe may di tu A den B : \(\dfrac{x}{25}\)
Thoi gian xe may di tu B ve A : \(\dfrac{x}{30}\)
Theo de ta co phuong trinh :
\(\dfrac{x}{25}-\dfrac{x}{30}=\dfrac{1}{3}\)
MTC : 150
\(\dfrac{6x}{150}-\dfrac{5x}{150}=\dfrac{50}{150}\)
Suy ra : 6x - 5x = 50
\(\Leftrightarrow\) x = 50 (km)
Vay quang duong AB dai 50 km
Chuc ban hoc tot
II: Tự luận
Câu 1:
a) Ta có: 2x-3=0
\(\Leftrightarrow2x=3\)
hay \(x=\dfrac{3}{2}\)
Vậy: \(S=\left\{\dfrac{3}{2}\right\}\)
b) Ta có: \(\dfrac{x+3}{3}< \dfrac{5-x}{3}\)
\(\Leftrightarrow\dfrac{x+3}{3}+\dfrac{x-5}{3}< 0\)
\(\Leftrightarrow2x-2< 0\)
\(\Leftrightarrow2x< 2\)
hay x<1
Vậy: S={x|x<1}
c) ĐKXĐ: \(x\notin\left\{1;2\right\}\)
Ta có: \(\dfrac{1}{x-1}-\dfrac{3}{x-2}=\dfrac{-1}{\left(x-1\right)\left(x-2\right)}\)
\(\Leftrightarrow\dfrac{x-2-3\left(x-1\right)}{\left(x-1\right)\left(x-2\right)}=\dfrac{-1}{\left(x-1\right)\left(x-2\right)}\)
Suy ra: \(x-2-3x+3=-1\)
\(\Leftrightarrow-2x+1=-1\)
\(\Leftrightarrow-2x=-2\)
hay x=1(loại)
Vậy: \(S=\varnothing\)
Câu 2:
Gọi x(km) là độ dài quãng đường AB(Điều kiện: x>0)
Thời gian người đó đi từ A đến B là:
\(\dfrac{x}{25}\left(h\right)\)
Thời gian người đó đi từ B về A là:
\(\dfrac{x}{30}\left(h\right)\)
Theo đề, ta có phương trình: \(\dfrac{x}{25}-\dfrac{x}{30}=\dfrac{1}{3}\)
\(\Leftrightarrow\dfrac{6x}{150}-\dfrac{5x}{150}=\dfrac{50}{150}\)
Suy ra: x=50(thỏa ĐK)
Vậy: AB=50km
