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Kham khảo nha
Tìm x biết: |x - 2010| + |x - 2012| + |x - 2014| = 4 - Toán học Lớp 7 - Bài tập Toán học Lớp 7 - Giải bài tập Toán học Lớp 7 | Lazi.vn - Cộng đồng Tri thức & Giáo dục
(x-2010)+(x-2012)+(x-2014)=4
x-2010+x-2012+x-2014=4
3x-6036=4
3x=6040
x=\(\frac{6040}{3}\)
a. |x-1|+ |x+3 | = 4
x-1+x+3=4
(x+x)-(1-3)=4
2x+2=4 ( trừ của trừ là cộng -(-2)=+2)
2x=4-2
x=2:2=1
b. |2x+4| -3|4-x|= -5
2x+4-3.4-x=-5
(2x-x)+4-(3.4)=-5
x+4-12=-5
x+4=-5+12
x+4=7
x=7-4=3
c. |x-2010|+|x-2012|+ |x-2014|=2
x-2010+x-2012+x-2014=2
(x+x+x)-(2010+2012+2014)=2
3x-6036=2
3x=2+6036
3x=6038
x=6038:3=3012
tick giùm đi nhé có j lần sau tui giải cho ^D^
b) \(\frac{x-99}{5}+\frac{x-97}{7}=\frac{x-95}{9}+\frac{x-93}{11}\)
\(\Leftrightarrow\left(\frac{x-99}{5}-1\right)+\left(\frac{x-97}{7}-1\right)=\left(\frac{x-95}{9}-1\right)\)\(+\left(\frac{x-93}{11}-1\right)\)
\(\Leftrightarrow\frac{x-104}{5}+\frac{x-104}{7}-\frac{x-104}{9}-\frac{x-104}{11}=0\)
\(\Leftrightarrow\left(x-104\right)\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)=0\)
Mà \(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\ne0\)
\(\Rightarrow x-104=0\)
\(\Leftrightarrow x=104\)
Vậy ....
a) \(\frac{x+1945}{45}+\frac{x+1954}{54}=\frac{x+1975}{75}+\frac{x+1969}{69}\)
\(\Leftrightarrow\left(\frac{x+1945}{45}-1\right)+\left(\frac{x+1954}{54}-1\right)=\left(\frac{x+1975}{75}-1\right)\)\(+\left(\frac{x+1969}{69}-1\right)\)
\(\Leftrightarrow\frac{x+1900}{45}+\frac{x+1900}{54}-\frac{x+1900}{75}-\frac{x+1900}{69}=0\)
\(\Leftrightarrow\left(x+1900\right)\left(\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\right)=0\)
Mà \(\frac{1}{45}+\frac{1}{54}-\frac{1}{75}-\frac{1}{69}\ne0\)
\(\Rightarrow x+1900=0\)
\(\Leftrightarrow x=-1900\)
Vậy ...
=20122011-2012.20122010+2012.20122009-.......................-2012.20122-1
còn lại tự làm nhá
1) \(\frac{x+1}{15}+\frac{x+2}{14}=\frac{x+3}{13}+\frac{x+4}{12}\)
\(\Leftrightarrow\frac{x+16}{15}+\frac{x+16}{14}-\frac{x+16}{13}-\frac{x+16}{12}=0\)
\(\Leftrightarrow\left(x+16\right)\left(\frac{1}{15}+\frac{1}{14}-\frac{1}{13}-\frac{1}{12}\right)=0\)
\(\Leftrightarrow x=-16\)
2)3)4) tương tự
Gợi ý : 2) cộng 3 vào cả hai vế
3)4) cộng 2 vào cả hai vế
5) \(\frac{x+1}{20}+\frac{x+2}{19}+\frac{x+3}{18}=-3\)
\(\Leftrightarrow\frac{x+21}{20}+\frac{x+21}{19}+\frac{x+21}{18}=0\)
\(\Leftrightarrow\left(x+21\right)\left(\frac{1}{20}+\frac{1}{19}+\frac{1}{18}\right)=0\)
\(\Leftrightarrow x=-21\)
6) sửa VT = 4 rồi tương tự câu 5)
Ta có :
\(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+8}{2010}+\frac{x+7}{2011}\)
\(\Leftrightarrow\)\(\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+8}{2010}+1\right)+\left(\frac{x+7}{2011}+1\right)\)
\(\Leftrightarrow\)\(\frac{x+4+2014}{2014}+\frac{x+3+2015}{2015}=\frac{x+8+2010}{2010}+\frac{x+7+2011}{2011}\)
\(\Leftrightarrow\)\(\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2010}+\frac{x+2018}{2011}\)
\(\Leftrightarrow\)\(\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2010}-\frac{x+2018}{2011}=0\)
\(\Leftrightarrow\)\(\left(x-2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)
Vì \(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2010}-\frac{1}{2011}\ne0\)
Nên \(x-2018=0\)
\(\Leftrightarrow\)\(x=2018\)
Vậy \(x=2018\)
Chúc bạn học tốt ~
Ta có: \(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+7}{2011}+\frac{x+8}{2010}\)
\(\Rightarrow\left(\frac{x+4}{2014}+1\right)+\left(\frac{x+3}{2015}+1\right)=\left(\frac{x+7}{2011}+1\right)+\left(\frac{x+8}{2010}+1\right)\)
\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2013}=\frac{x+2018}{2011}+\frac{x+2018}{2010}\)
\(\Rightarrow\frac{x+2018}{2014}+\frac{x+2018}{2013}-\frac{x+2018}{2011}-\frac{x+2018}{2010}=0\)
\(\Rightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
\(\Rightarrow x+2018=0\Rightarrow x=-2018\)
Chúc bn hc tốt! ^_^
Tham khảo ở đây nhé bn: olm.vn/hoi-dap/question/686545.html, mk lm r`
ta có \(\hept{\begin{cases}\left(2x-1\right)^{2012}\ge0\\\left(3y+2\right)^2\ge0\end{cases}}\)
+ hết vào ta có VT>=0
từ bpt => VT=0 <=> x = 1/2 và y=-2/3
bạn MAi thị diệu linh ơi, cho mik hỏi bài mik làm sai chỗ nào vậy bạn
\(\frac{x+4}{2012}+\frac{x+3}{2013}=\frac{x+2}{2014}+\frac{x+1}{2015}.\)
\(\left(\frac{x+4}{2012}+1\right)+\left(\frac{x+3}{2013}+1\right)=\left(\frac{x+2}{2014}+1\right)+\left(\frac{x+1}{2015}+1\right)\)
\(\left(\frac{x+4}{2012}+\frac{2012}{2012}\right)+\left(\frac{x+3}{2013}+\frac{2013}{2013}\right)=\left(\frac{x+2}{2014}+\frac{2014}{2014}\right)+\left(\frac{x+1}{2015}+\frac{2015}{2015}\right)\)
\(\frac{x+2016}{2012}+\frac{x+2016}{2013}=\frac{x+2016}{2014}+\frac{x+2016}{2015}\)
\(\frac{x+2016}{2012}+\frac{x+2016}{2013}-\frac{x+2016}{2014}-\frac{x+2016}{2015}=0\)
\(\left(x+2016\right)\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}-\frac{1}{2015}\right)=0\)
\(\Rightarrow x+2016=0\Rightarrow x=\left(-2016\right)\)
Có\(\left|x-2010\right|+\left|x-2012\right|+\left|x-2014\right|\ge\left|x-2010+2014-x\right|+\left|x-2012\right|\ge2\)
mà\(\left|x-2010\right|+\left|x-2012\right|+\left|x-2014\right|=2\)
dấu "=' \(\Leftrightarrow\left\{{}\begin{matrix}x-2012=0\\2010\le x\le2014\end{matrix}\right.\)\(\Rightarrow x=2012\)
Thay vào thì \(|x-2010|+|x-2012|+|x-2014|=4\) (Vô lý)