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ta có :
(2x-1)6>hoặc = 0
(2x-1)8>hoặc = 0
mà (2x-1)6 = (2x-1)8nên :
2x-1=0
2x=0+1
2x=1
=> x=1\2
Ta có :
2x + \(\frac{1}{3}\)x + 5 = \(\frac{3}{7}\)
x . (2 + \(\frac{1}{3}\)) = \(\frac{3}{7}\)- 5
x . \(\frac{7}{3}\)= \(\frac{-32}{7}\)
x = \(\frac{-32}{7}\)\(:\)\(\frac{7}{3}\)\(=\)\(\frac{-96}{49}\)
6/3x +1/3x +5 -3/7= 0
7x +35/7 -3/7= 0
7x +32= 0
x= -4.57 ( xấp xỉ)
(2x- 3)2 = 16
=>\(\hept{\begin{cases}2x-3=4\\2x-3=-4\end{cases}}\)
=>\(\hept{\begin{cases}2x=7\\2x=-1\end{cases}}\)
=>\(\frac{ }{\hept{\begin{cases}x=3,5\\x=-0,5\end{cases}}}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\frac{x+1}{2}=\frac{y+3}{4}\)\(=\frac{z+5}{6}\)\(=\frac{2.\left(x+1\right)+3.\left(y+3\right)+4.\left(z+5\right)}{2.2+3.4+4.6}\)
\(=\frac{2x+2+3y+9+4z+20}{4+12+24}\)\(=\frac{\left(2x+3y+4z\right)+\left(2+9+20\right)}{40}\)
\(=\frac{9+31}{40}=\frac{40}{40}=1\)
Cứ thế là tìm x+1 rồi tìm x
y+3 y
x+5 z
a) Ta có: \(A=\left|3x+\frac{1}{3}\right|-\frac{1}{4}\ge-\frac{1}{4}\left(\forall x\right)\)
Dấu "=" xảy ra khi: \(\left|3x+\frac{1}{3}\right|=0\Rightarrow x=-\frac{1}{9}\)
Vậy Min(A) = -1/4 khi x = -1/4
b) Ta có: \(\frac{3}{4}-\left|2x-\frac{1}{2}\right|0\le\frac{3}{4}\left(\forall x\right)\)
Dấu "=" xảy ra khi: \(\left|2x-\frac{1}{2}\right|=0\Rightarrow x=\frac{1}{4}\)
Vậy Max(B) = 3/4 khi x = 1/4
a. Vì \(\left|3x+\frac{1}{3}\right|\ge0\forall x\)\(\Rightarrow A=\left|3x+\frac{1}{3}\right|-\frac{1}{4}\ge-\frac{1}{4}\)
Dấu "=" xảy ra \(\Leftrightarrow\left|3x+\frac{1}{3}\right|=0\Leftrightarrow3x+\frac{1}{3}=0\Leftrightarrow x=-\frac{1}{9}\)
Vậy minA = - 1/4 <=> x = - 1/9
b. Vì \(\left|2x-\frac{1}{2}\right|\ge0\forall x\)\(\Rightarrow B=\frac{3}{4}-\left|2x-\frac{1}{2}\right|\le\frac{3}{4}\)
Dấu "=" xảy ra \(\Leftrightarrow\left|2x-\frac{1}{2}\right|=0\Leftrightarrow2x-\frac{1}{2}=0\Leftrightarrow x=\frac{1}{4}\)
Vậy maxB = 3/4 <=> x = 1/4
\(\left(2x-3\right)^2=16\)
\(\Rightarrow\left(2x-3\right)^2=4^2\)
\(\Rightarrow2x-3=4\)
\(\Rightarrow2x=4+3\)
\(\Rightarrow2x=7\)
\(\Rightarrow x=\frac{7}{2}\)
a) \(\left|x-3\right|+\left|2x-6\right|=8\)
\(x-3+2x-6=8\)
\(3x-9=8\)
\(3x=17\)
\(\Rightarrow x=\frac{17}{3}\)
b) Tương tự câu a .
c) \(\left|2x-3\right|=6-\left|3-2x\right|\)
\(2x-3=6-3-2x\)
\(2x-3=x\)
\(-2x=3\)
\(x=\frac{-3}{2}\)
d) \(\left|3x-2\right|-\left|6-9x\right|=-\left|-16\right|\)
\(3x-2-6-9x=-16\)
\(3x-8-9x=-16\)
\(-6x-8=-16\)
\(-6x=-8\)
\(\Rightarrow x=\frac{8}{6}\)
\(\)
2x+3-|3-2x| (1)
TH1: 3-2x \(\ge0\)\(\Leftrightarrow|3-2x|=3-2x\)
(1) \(\Leftrightarrow\)2x+3-3+2x=4x
Vì 3-2x\(\ge\)0\(\Rightarrow\)-2x\(\ge\)-3\(\Leftrightarrow\)x\(\ge\frac{3}{2}\)
\(\Rightarrow4x\ge6\)
TH2:3-2x<0\(\Leftrightarrow\)|3-2x|=2x-3
(1)\(\Leftrightarrow\)2x+3-2x+3=6
Vậy GTLN 2x+3-|3-2x|=6