1) x+14=43x+14=43

⇒x=43−14=1312⇒x=43−14=1312

2) 34:25.x=296034:25.x=2960

⇒25.x=2960−34=−415⇒25.x=2960−34=−415

⇒x=−415.52=−23⇒x=−415.52=−23

3) 134.x+112=−45134.x+112=−45

⇒74.x+32=−45⇒74.x+32=−45

⇒74.x=−45−32=−2310⇒74.x=−45−32=−2310

⇒x=−2310.47=−−4635⇒x=−2310.47=−−4635

4) 1112−(25+x)=231112−(25+x)=23

⇒25+x=1112−23=14⇒25+x=1112−23=14

⇒x=14−25=−320⇒x=14−25=−320

5) 234.x=317:0,01234.x=317:0,01

⇒114.x=117:1100=11007⇒114.x=117:1100=11007

⇒x=11007.411=447⇒x=11007.411=447

6) 2x.(x−17)=02x.(x−17)=0

⇒x−17=0⇒x−17=0 (1) hoặc x=0x=0

(1) ⇒x=17⇒x=17

Vậy x={0;17}x={0;17}

7) 34+14:x=2534+14:x=25

⇒14:x=25−34=−720⇒14:x=25−34=−720

⇒x=14:−720=14.−207=−57⇒x=14:−720=14.−207=−57

8) 3,8:2x=14:2233,8:2x=14:223

⇒1,9x=14:83=14.38=332⇒1,9x=14:83=14.38=332

⇒x=332:1,9=15304⇒x=332:1,9=15304

9) 0,25x:3=56:0,125=56:18=56.8=2030,25x:3=56:0,125=56:18=56.8=203

⇒0,25x=203.3=20⇒0,25x=203.3=20

⇒x=20:0,25=80⇒x=20:0,25=80

10) 113:0,8=23:0,1x113:0,8=23:0,1x

⇒43:45=23:110.x⇒43:45=23:110.x

⇒53=203.x⇒53=203.x

⇒x=53:203=14⇒x=53:203=14

11) 3,2x+(−1,2)x+2,7=−4,93,2x+(−1,2)x+2,7=−4,9

⇒2x+2,7=−4,9⇒2x+2,7=−4,9

⇒2x=−4,9−2,7=−7,6⇒2x=−4,9−2,7=−7,6

⇒x=−3,8⇒x=−3,8

12) |x|−2,2=1,3|x|−2,2=1,3

⇒|x|=1,3+2,2=3,5⇒|x|=1,3+2,2=3,5

⇒x=±3,5⇒x=±3,5

13) |x+34|−13=0|x+34|−13=0

⇒|x+34|=13⇒|x+34|=13

⇒x+34=13⇒x=−512⇒x+34=13⇒x=−512

hoặc x+34=−13⇒x=−1312x+34=−13⇒x=−1312

Vậy x={−512;−1312}x={−512;−1312}

14) |x+13|−4=−1|x+13|−4=−1

⇒|x+13|=−1+4=3⇒|x+13|=−1+4=3

⇒x+13=3⇒x=83⇒x+13=3⇒x=83

Hoặc x+13=−3⇒x=−3−13=−103x+13=−3⇒x=−3−13=−103

15) Do |x−1,5|≥0|x−1,5|≥0 và |2,5−x|≥0|2,5−x|≥0 với mọi giá trị của xx

⇒|x−1,5|+|2,5−x|=0⇒|x−1,5|+|2,5−x|=0 khi 

⇒x−1,5=0⇒x=1,5⇒x−1,5=0⇒x=1,5 và 2,5−x=0⇒x=2,52,5−x=0⇒x=2,5 (loại vì ra 2 kết quả khác nhau)

Xin lỗi,em không giúp được 

2-4+4,4-4.7+7.65-78+87= 14,35

Câu 3: 

\(3^{417}>3^{400}=\left(3^4\right)^{100}=81^{100}\)

\(4^{278}< 4^{300}=\left(4^3\right)^{100}=64^{100}\)

Có \(81>64\)nên \(81^{100}>64^{100}\)

Suy ra \(3^{417}>4^{278}\).

Câu 4: 

\(A=5^{x+1}+5^{x+2}+5^{x+3}+...+5^{x+120}\)

\(=5^x\left(5+5^2+...+5^{119}\right)\)

\(=5^x\left[\left(5+5^2+5^3+5^4\right)+...+\left(5^{117}+5^{118}+5^{119}+5^{120}\right)\right]\)

\(=5^x\left[\left(5+5^2+5^3+5^4\right)+...+5^{116}\left(5+5^2+5^3+5^4\right)\right]\)

\(=5^x\left(1+...+5^{116}\right)\left(5+5^2+5^3+5^4\right)=5^x\left(1+...+5^{116}\right).780\)

chia hết cho \(780\). 

a) \(\frac{1}{8}-\left(x-\frac{1}{2}\right)=\frac{1}{\sqrt{9}}\)

\(\Rightarrow\frac{1}{8}-\left(x-\frac{1}{2}\right)=\frac{1}{3}\)

\(\Rightarrow x-\frac{1}{2}=\frac{1}{8}-\frac{1}{3}\)

\(\Rightarrow x-\frac{1}{2}=\frac{-5}{24}\)

\(\Rightarrow x=\frac{7}{24}\)

b) \(\left|\frac{5}{18}-x\right|+\frac{1}{5}=\frac{1}{2}\)

\(\Rightarrow\left|\frac{5}{18}-x\right|=\frac{3}{10}\)

\(\Rightarrow\orbr{\begin{cases}\frac{5}{18}-x=\frac{3}{10}\\\frac{5}{18}-x=-\frac{3}{10}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{5}{18}-\frac{3}{10}\\x=\frac{5}{18}+\frac{3}{10}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-1}{45}\\x=\frac{26}{45}\end{cases}}\)