a ) 10 x X - 1 - 3 - 5 - 7 - ... - 19 = 2 + 4 + 6 + ... + 20

10 x X - 1 - 3 - 5 - 7 - ... - 19 = 110

10 x X - ( 1 + 3 + 5 + 7 + ... + 19 ) = 110

10 x X - 100 = 110

10 x X = 110 + 100

10 x X = 210

       X = 210 : 10

       X = 21

a 10 x X-1-3-5-7-....-19 = 2+4+6+....+20

​10xX-1-3-5-7-....-19=110

​10xX=110+1+3+5+7+....+19

​10xX=210

​X=210:10

​X=21

b là 4

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1: Ta có: |-3x|=x+5

\(\Leftrightarrow\left[{}\begin{matrix}-3x=x+5\left(x\le0\right)\\3x=x+5\left(x>0\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-3x-x=5\\3x-x=5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-4x=5\\2x=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-5}{4}\left(nhận\right)\\x=\dfrac{5}{2}\left(nhận\right)\end{matrix}\right.\)

Vậy: \(S=\left\{-\dfrac{5}{4};\dfrac{5}{2}\right\}\)

2: Ta có: \(10-\left|x+1\right|=3x+5\)

\(\Leftrightarrow\left|x+1\right|=10-3x-5\)

\(\Leftrightarrow\left|x+1\right|=-3x+5\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=-3x+5\left(x\ge-1\right)\\-x-1=-3x+5\left(x< -1\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+3x=5-1\\-x+3x=5+1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=4\\2x=6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\left(nhận\right)\\x=3\left(loại\right)\end{matrix}\right.\)

Vậy:S={1}

3: Ta có: \(\dfrac{2x+3}{-4}\ge\dfrac{4-x}{-3}\)

\(\Leftrightarrow\dfrac{-2x-3}{4}\ge\dfrac{x-4}{3}\)

Suy ra: \(3\left(-2x-3\right)\ge4\left(x-4\right)\)

\(\Leftrightarrow-6x-9-4x+16\ge0\)

\(\Leftrightarrow-10x\ge-7\)

hay \(x\le\dfrac{7}{10}\)

Vậy: S={x|\(x\le\dfrac{7}{10}\)}

3\(x\)(- \(\dfrac{4}{3}\)\(x\) + 1) - 4\(x\).(\(x\) - 2) = 10

-4\(x^2\) + 3\(x\) - 4\(x^2\) + 3\(x\) + 8\(x\) = 10

-8\(x^2\) + 14\(x\) - 10 = 0

4\(x^2\) + 7\(x\) - 5 = 0

4.(\(x^2\) + 2.\(\dfrac{7}{8}\) + \(\dfrac{49}{64}\)) - \(\dfrac{129}{16}\) = 0

4.(\(x\) + \(\dfrac{7}{8}\))²  = \(\dfrac{129}{16}\)

   (\(x\) + \(\dfrac{7}{8}\))² =  \(\dfrac{129}{16}\)

    \(x\)           = \(\dfrac{\pm\sqrt{129}-7}{8}\)

a)

\(3^x+3^{x+1}+3^{x+2}=117\\ \Leftrightarrow3^x+3.3^x+9.3^x=117\\ 13.3^x=117\\ \Leftrightarrow3^x=9\\ \Leftrightarrow3^x=3^2\\ \Leftrightarrow x=2\)

b)

 \(3+4\left(x-10\right)=3^2+6\\ \Leftrightarrow3+4\left(x-10\right)=15\\ \Leftrightarrow4\left(x-10\right)=12\\ \Leftrightarrow x-10=3\\ \Leftrightarrow x=13\)

a) \(3^x+3^{x+1}+3^{x+2}=117\)

\(3^x+3^x.3+3^x.3^2=117\)

\(3^x.\left(1+3+3^2\right)=117\)

\(3^x.13=117\)

\(3^x=9\)

\(x=2\)

b) \(3+4\left(x-10\right)=3^2+6\)

\(3+4x-40=9+6\)

\(4x=15+40-3\)

\(4x=52\)

\(x=13\)

\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{\left(3x-1\right).\left(3x+3\right)}=\frac{3}{10}\)

=> \(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{3x-1}-\frac{1}{3x+3}=\frac{3}{10}\)

=> \(\frac{1}{3}-\frac{1}{3x+3}=\frac{3}{10}\)

=> \(\frac{1}{3x+3}=\frac{1}{3}-\frac{3}{10}\)

=> \(\frac{1}{3x+3}=\frac{1}{30}\)

=> 3x + 3 = 30

=> 3.(x + 1) = 30

=> x + 1 = 10

=> x = 9

x = 9 nha bạn

a) \(\left(3x-2\right)\left(3x+2\right)-\left(3x+4\right)^2=20\\ \Rightarrow9x^2-4-9x^2-24x-16-20=0\\ \Rightarrow-24x-40=0\\ \Rightarrow-24x=40\\ \Rightarrow x=-\dfrac{5}{3}\)

b) \(6x^2-2x\left(3x+1\right)=10\\ \Rightarrow6x^2-6x^2-2x=10\\ \Rightarrow-2x=10\\ \Rightarrow x=-5\)

c) \(x^2+4x+3=0\\ \Rightarrow\left(x+1\right)\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+1=0\\x+3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\)

4x² + 3x - 4x² + 8x - 10 = 0

11x - 10 = 0

x = 10/11

\(3x\left(\dfrac{4}{3}x+1\right)-4x\left(x-2\right)=10\)

\(\Leftrightarrow4x^2+3x-4x^2+8x=10\)

\(\Leftrightarrow x=\dfrac{10}{11}\)

\(3x\left(\dfrac{4}{3}x+1\right)-4x\left(x-2\right)=10\\ \Leftrightarrow4x^2+3x-4x^2+8x=10\\ \Leftrightarrow11x=10\Leftrightarrow x=\dfrac{10}{11}\)

a) x= chịu

b) x=2

(3x-4)³ = 7 + 1²⁰²¹

( 3x - 4 )³= 7 + 1

( 3x - 4 )³= 8

( 3x - 4 )³= 2³

⇒3x - 4 = 2

⇒3x = 2+4

   3x = 6

      x= 6:3

      x=2

Mình chỉ bt làm câu 2 thôi câu 1 tớ ko bt thông cảm nhé :)))

câu đầu tiên thấy kì kì

x=2

nik lộn

2^x+1. 2^{2009 =} 2²⁰¹⁰

10 - 2x = 25 - 3x

a: =-3/4-1/4+2/7+5/7+2023/2024

=-1+1+2023/2024=2023/2024

b: 2/3x=2/7

=>x=2/7:2/3=3/7

c; =>2/3x=1/10+1/2=1/10+5/10=6/10=3/5

=>x=3/5:2/3=3/5*3/2=9/10