\(a,-12\left(x-5\right)+7\left(3-x\right)=5\)

\(-12x+60+21-7x=5\)

\(-12x-7x=5-60-21\)

\(-19x=-76\Leftrightarrow x=4\)

\(b,30\left(x+2\right)-6\left(x-5\right)-24x=100\)

\(30x+60-6x+30-24x=100\)

\(30x-6x-24x=100-60-30\)

\(0x=10\left(vl\right)\)

Vậy pt vô nghiệm 

\(c,\left(x-23\right):14+25=42-1^{2002}\)

\(\left(x-23\right).\frac{1}{14}+25=42-1\)

\(\frac{x}{14}-\frac{23}{14}+25=41\)

\(\frac{x}{14}-\frac{23}{14}=16\)

\(\frac{x}{14}=\frac{247}{14}\)

\(x=247\)

a) \(\frac{x-1}{2015}+\frac{x-2}{2014}=\frac{x-3}{2013}+\frac{x-4}{2012}\)

\(\Rightarrow\left(\frac{x-1}{2015}-1\right)+\left(\frac{x-2}{2014}-1\right)=\left(\frac{x-3}{2013}-1\right)+\left(\frac{x-4}{2012}-1\right)\)

\(\Rightarrow\frac{x-2016}{2015}+\frac{x-2016}{2014}=\frac{x-2016}{2013}+\frac{x-2016}{2012}\)

\(\Rightarrow\frac{x-2016}{2015}+\frac{x-2016}{2014}-\frac{x-2016}{2013}-\frac{x-2016}{2012}=0\)

\(\Rightarrow\left(x-2016\right).\left(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\right)=0\)

Vì \(\frac{1}{2015}+\frac{1}{2014}-\frac{1}{2013}-\frac{1}{2012}\ne0\Rightarrow x-2016=0\)

\(\Rightarrow x=2016\)

b) \(\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}=\frac{x-4}{2001}\)

\(\Rightarrow\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}-\frac{x-4}{2001}=0\)

\(\Rightarrow\left(\frac{x-1}{2004}-1\right)+\left(\frac{x-2}{2003}-1\right)-\left(\frac{x-3}{2002}-1\right)-\left(\frac{x-4}{2001}-1\right)=0\)

\(\Rightarrow\frac{x-2005}{2004}+\frac{x-2005}{2003}-\frac{x-2005}{2002}-\frac{x-2005}{2001}=0\)

\(\Rightarrow\left(x-2005\right)\left(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\right)=0\)

vì \(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\ne0\Rightarrow x-2005=0\)

\(\Rightarrow x=2005\)

c) \(|5x-3|\ge7\)

\(\Rightarrow5x-3\ge7\) hoặc - (5x-3) \(\ge7\)

\(\Rightarrow5x-3\ge7\) hoặc \(-5x+3\ge7\)

\(\Rightarrow5x\ge10\) hoặc \(-5x\ge4\)

\(\Rightarrow x\ge2\) hoặc \(x\le\frac{4}{-5}\)

k nhé!!! Kp luôn nha!

Bài 1:

199²⁰ < 200²⁰ = (2³ . 5²)²⁰ = 2⁶⁰ . 5⁴⁰

 2003¹⁵ > 2000¹⁵ = (2⁴ . 5³)¹⁵ = 2⁶⁰ . 5⁴⁵

Do: 2⁶⁰ . 5⁴⁰ < 2⁶⁰ . 5⁴⁵  => 199²⁰ < 2⁶⁰ . 5⁴⁰ < 2⁶⁰ . 5⁴⁵ < 2003¹⁵  => 199²⁰ < 2003¹⁵

Bài 2:

a/ (3 . x - 9) . 3¹² = 3¹⁵   => 3 . x - 9 = 3¹⁵ : 3¹²

=> 3 . x - 9 = 27     => 3 . x = 27 + 9

=> 3 . x = 36   => x = 12

b/ (7 . x + 6) . 5⁵ = 5⁸  => 7 . x + 6 = 5⁸ : 5⁵

=> 7 . x + 6 = 125  => 7 . x = 125 - 6

=> 7 . x = 119  => x = 17

c/ (x - 5)⁴ = (x - 5)⁶

<=> x - 5 = 1 hoặc x - 5 = -1 hoặc x - 5 = 0

=> x = 6 hoặc x = 4 hoặc x = 5

bài 1:

a) (x+1)^2-(x-1)^2-3(x+1)(x-1)

=(x+1+x-1)(x+1-x+1)-3x^2-3

=2x^2-3x^2-3

=-x^2-3

\(x+\left(x+1\right)+....+2003=2003\Leftrightarrow x+\left(x+1\right)+....+2002=0\)

\(\Leftrightarrow\left(2002+x\right)\left(2002-x+1\right)=0\Leftrightarrow\left(2002+x\right)\left(2003-x\right)=0\Leftrightarrow\orbr{\begin{cases}x=-2002\\x=2003\end{cases}}\)

\(\left(x+1\right)+\left(x+3\right)+.....+\left(x+99\right)=0\)

\(\Leftrightarrow45x+\left(1+3+...+99\right)=0\Leftrightarrow45x+\frac{100.45}{2}=0\Leftrightarrow x+50=0\Leftrightarrow x=-50\)

Trl

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