1: \(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{20}{15}=\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac13-\frac43\right)=1-1=0\)

2: \(2\frac56+\frac16:\left(-\frac58\right)=\frac{17}{6}+\frac16\cdot\frac{-8}{5}=\frac{17}{6}-\frac{8}{30}=\frac{85-8}{30}=\frac{77}{30}\)

3: \(3-\frac32+\frac14-1\frac15=\frac32+\frac14-\frac65\)

\(=\frac{30}{20}+\frac{5}{20}-\frac{24}{20}=\frac{35-24}{20}=\frac{11}{20}\)

4: \(5^3:25+2^4:4=\frac{125}{25}+\frac{16}{4}=5+4=9\)

5: \(23\frac14:\frac75-13\frac14:\frac75=\left(23+\frac14-13-\frac14\right):\frac75=10\cdot\frac57=\frac{50}{7}\)

6: \(12\frac15\cdot\frac45-22\frac15\cdot\frac45=\left(12+\frac15-22-\frac15\right)\cdot\frac45=-10\cdot\frac45=-8\)

7: \(\left(-2\right)^2+\sqrt{49}-\sqrt{16}+\sqrt{25}=4+7-4+5=7+5=12\)

8: \(\frac45-\left(-\frac12\right)^2=\frac45-\frac14=\frac{16}{20}-\frac{5}{20}=\frac{11}{20}\)

9: \(5-\left(-\frac57\right)^0+\left(\frac13\right)^2:3=5-1+\frac{1}{27}=4+\frac{1}{27}=\frac{109}{27}\)

10: \(\frac29\left(\frac52-\frac34\right)=\frac29\left(\frac{10}{4}-\frac34\right)=\frac29\cdot\frac74=\frac{7}{9\cdot2}=\frac{7}{18}\)

11: \(16\cdot\left(-\frac14\right)^3-\frac12=16\cdot\frac{-1}{64}-\frac12=-\frac14-\frac12=-\frac34\)

d d c b c b b a b c

wow

đúng là ctv

3. gọi tử là x

         mẫu là x + 8

Nếu thêm vào tử và bớt mẫu:

 tử là  x+2

mẫu là x+5

Ta có: \(\dfrac{x+2}{x+5}\)=\(\dfrac{3}{4}\)

          4(x+2)=3(x+5)

          4x + 8 = 3x + 15

          x = 7

Tử số là 7
Mẫu số là x+8= 7+8= 15

Vậy phân số ban đầu l: \(\dfrac{7}{15}\)

2. \(\dfrac{3\left(x-2\right)}{6}\)- \(\dfrac{4}{6}\)> \(\dfrac{6x}{6}\)-\(\dfrac{6}{6}\)

<=> 3x - 6 - 4> 6x - 6

<=> 3x - 6 - 4 - 6x + 6> 0

<=> -3x -4 > 0

<=> -3x >  4

<=> x < \(\dfrac{-4}{3}\)

S= {x/x <\(\dfrac{-4}{3}\)}

trục số bạn tự vẽ giúp mình nhé

câu 5 : B 

Câu 5 ) b                                                                                          Câu 6 ) b . ok nhé

b a c c c c c a d d d b b c a b

giải nhanh như thế chắc học tốt GDCD lắm nhể???

1

a

\(A=x^2-2x+4=x^2-2x+1+3\\=\left(x-1\right)^2+3\ge3\)

Min A = 3 khi và chỉ khi `x=1`

b

\(B=x^2+4x+5=x^2+4x+4+1\\ =\left(x+2\right)^2+1\ge1\)

Min B = 1 khi và chỉ khi `x=-2`

c

\(C=x^2+3x+4=x^2+3x+\dfrac{9}{4}+\dfrac{7}{4}\\ =\left(x+\dfrac{3}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\)

Min C = \(\dfrac{7}{4}\) khi và chỉ khi \(x=-\dfrac{3}{2}\)

d

\(D=3x^2-6x+4=3\left(x^2-2x+\dfrac{4}{3}\right)\\ =3\left(x^2-2x+1+\dfrac{1}{3}\right)\\ =3\left(x-1\right)^2+3.\dfrac{1}{3}\ge3.\dfrac{1}{3}\)

Min D = 1 khi và chỉ khi `x=1`

Bài 6

a) x + 0,5 = 2/3

x + 1/2 = 2/3

x = 2/3 - 1/2

x = 1/6

b) 1/5 + (x - 2/3) = 5/3

x - 2/3 = 5/3 - 1/5

x - 2/3 = 22/15

x = 22/15 + 2/3

x = 32/15

c) (5/6 x + 3)² = 25/36

5/6 x + 3 = 5/6 hoặc 5/6 x + 3 = -5/6

*) 5/6 x + 3 = 5/6

5/6x = 5/6 - 3

5/6 x = -13/6

x = -13/6 : 5/6

x = -13/5

*) 5/6 x + 3 = -5/6

5/6 x = -5/6 - 3

5/6 x = -23/6

x = -23/6 : 5/6

x = -23/5

Vậy x = -23/5; x = -13/5

e) 2.|x - 1/8| = 6

|x - 1/8| = 6 : 2

|x - 1/8| = 3

*) Với x ≥ 1/8, ta có:

x - 1/8 = 3

x = 3 + 1/8

x = 25/8 (nhận)

*) Với x < 1/8, ta có:

x - 1/8 = -3

x = -3 + 1/8

x = -23/8 (nhận)

Vậy x = -23/8; x = 25/8

5:

2: \(\left|3x-5\right|-\dfrac{1}{7}=\dfrac{1}{3}\)

=>\(\left|3x-5\right|=\dfrac{1}{3}+\dfrac{1}{7}=\dfrac{10}{21}\)

=>\(\left[{}\begin{matrix}3x-5=\dfrac{10}{21}\\3x-5=-\dfrac{10}{21}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=\dfrac{115}{21}\\3x=-\dfrac{10}{21}+\dfrac{105}{21}=\dfrac{95}{21}\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=\dfrac{115}{63}\\x=\dfrac{95}{63}\end{matrix}\right.\)

3:

\(\left(\dfrac{3}{5}x-\dfrac{2}{3}x-x\right)\cdot\dfrac{1}{7}=\dfrac{-5}{21}\)

=>\(x\left(\dfrac{3}{5}-\dfrac{2}{3}-1\right)=\dfrac{-5}{21}:\dfrac{1}{7}=\dfrac{-5}{21}\cdot7=-\dfrac{5}{3}\)

=>\(x\cdot\dfrac{9-10-15}{15}=\dfrac{-5}{3}\)

=>\(x\cdot\dfrac{-16}{15}=\dfrac{-5}{3}\)

=>\(x=\dfrac{5}{3}:\dfrac{16}{15}=\dfrac{5}{3}\cdot\dfrac{15}{16}=\dfrac{75}{48}=\dfrac{25}{16}\)

5:

\(0,2+\left|x-2,3\right|=1,1\)

=>\(\left|x-2,3\right|=1,1-0,2=0,9\)

=>\(\left[{}\begin{matrix}x-2,3=0,9\\x-2,3=-0,9\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=2,3+0,9=3,2\\x=2,3-0,9=1,4\end{matrix}\right.\)

6: \(5\left(x+2\right)^3+7=2\)

=>\(5\left(x+2\right)^3=-5\)

=>\(\left(x+2\right)^3=-1\)

=>x+2=-1

=>x=-3

8: \(14-\left|\dfrac{3}{2}x-1\right|=9\)

=>\(\left|\dfrac{3}{2}x-1\right|=14-9=5\)

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

=>\(\left[{}\begin{matrix}x=6:\dfrac{3}{2}=6\cdot\dfrac{2}{3}=4\\x=-4:\dfrac{3}{2}=-4\cdot\dfrac{2}{3}=-\dfrac{8}{3}\end{matrix}\right.\)