a, Có : |2x-1| + |2x-5| = |2x-1| + |5-2x| >= |2x-1+5-2x| = 4

Dấu "=" xảy ra <=> (2x-1).(5-2x) = 0 <=> 1/2 < = x < = 5/2

Vậy 1/2 < = x < = 5/2

b, +, Nếu x < -3/4 => 3-x-3x-4 = -2x-1

=> ko tồn tại x

+, Nếu -3/4 < = x < = -1/2 => 3-x+3x+4 = -2x-1

=> x=-2 ( ko t/m )

+, Nếu -1/2 < x < = 3 => 3-x+3x+4=2x+1

=>ko tồn tại x

+, Nếu x > 3 => x-3+3x+4=2x+1

=> x=0 ( ko t/m )

Vậy ko tồn tại x t/m bài toán

Tham khảo xem có đúng ko nha !

số số hạng là :

( 2500 - 2 ) : 2 + 1 = 1250 ( số )

Tổng dãy trên là :

( 2500 + 2 ) x 1250 : 2 = 1563750 

Đ/S : 1563750

`@` `\text {Ans}`

`\downarrow`

`1)`

\(2x+\dfrac{1}{2}=\dfrac{5}{3}\)

`\Rightarrow`\(2x=\dfrac{5}{3}-\dfrac{1}{2}\)

`\Rightarrow`\(2x=\dfrac{7}{6}\)

`\Rightarrow`\(x=\dfrac{7}{6}\div2\)

`\Rightarrow`\(x=\dfrac{7}{12}\)

Vậy, `x = 7/12`

`2)`

\(\dfrac{1}{7}+\dfrac{4}{5}x=\dfrac{5}{3}\)

`\Rightarrow`\(\dfrac{4}{5}x=\dfrac{5}{3}-\dfrac{1}{7}\)

`\Rightarrow`\(\dfrac{4}{5}x=\dfrac{32}{21}\)

`\Rightarrow`\(x=\dfrac{32}{21}\div\dfrac{4}{5}\)

`\Rightarrow`\(x=\dfrac{40}{21}\)

Vậy, `x = 40/21`

`3)`

\(\dfrac{3}{5}-\dfrac{3}{5}x=\dfrac{1}{7}\)

`\Rightarrow`\(\dfrac{3}{5}x=\dfrac{3}{5}-\dfrac{1}{7}\)

`\Rightarrow`\(\dfrac{3}{5}x=\dfrac{16}{35}\)

`\Rightarrow`\(x=\dfrac{16}{35}\div\dfrac{3}{5}\)

`\Rightarrow`\(x=\dfrac{16}{21}\)

Vậy, `x = 16/21`

`4)`

\(\dfrac{5}{6}-3x=\dfrac{3}{4}\)

`\Rightarrow`\(3x=\dfrac{5}{6}-\dfrac{3}{4}\)

`\Rightarrow`\(3x=\dfrac{1}{12}\)

`\Rightarrow`\(x=\dfrac{1}{12}\div3\)

`\Rightarrow`\(x=\dfrac{1}{36}\)

Vậy, `x  = 1/36`

`5)`

\(\dfrac{5}{3}-\dfrac{1}{2}x=\dfrac{3}{7}\)

`\Rightarrow`\(\dfrac{1}{2}x=\dfrac{5}{3}-\dfrac{3}{7}\)

`\Rightarrow`\(\dfrac{1}{2}x=\dfrac{26}{21}\)

`\Rightarrow`\(x=\dfrac{26}{21}\div\dfrac{1}{2}\)

`\Rightarrow`\(x=\dfrac{52}{21}\)

Vậy, `x = 52/21`

`6)`

\(5x+\dfrac{1}{2}=\dfrac{2}{3}\)

`\Rightarrow`\(5x=\dfrac{2}{3}-\dfrac{1}{2}\)

`\Rightarrow`\(5x=\dfrac{1}{6}\)

`\Rightarrow`\(x=\dfrac{1}{6}\div5\)

`\Rightarrow`\(x=\dfrac{1}{30}\)

Vậy, `x = 1/30.`

Tính phải k nhỉ?

`1)`

`2x + 3x + 5x`

`= (2 + 3 + 5)x`

`= 10x`

`2)`

`2.x - x + 3.x`

`= (2 - 1 + 3)x`

`= 4x`

`3)`

`9.x - 3 - 3.x`

`= (9 - 3)x - 3`

`= 6x - 3`

`4)`

Thiếu dấu, bạn bổ sung thêm

`5)`

`x - 0,2x - 0,1x`

`= (1 - 0,2 - 0,1)x`

`=0,7x`

`6)`

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

e) 1/3+1/3:x=1

1/3:x=1-1/3

1/3:x=2/3

x=1/3:2/3

x=1/2

f) x:3/4+1/4=-2/3

x:3/4=-2/3-1/4

x:3/4=-11/12

x=-11/12.3/4

x=-11/16

g) x:(1/2+1/3)=6/5

x:5/6=6/5

x=6/5.5/6

x=1

\(a)x^2-5x+6\)

\(=x^2-2x-3x+6\)

\(=x\left(x-2\right)-3\left(x-2\right)\)

\(=\left(x-2\right)\left(x-3\right)\)

\(b)x^3-5x^2+8x-4\)

\(=x^3-x^2+x^2-5x^2+8x-4\)

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

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

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

\(=\left(x-1\right)\left(x-2\right)^2\)

\(c)x^2-5x-14\)

\(=x^2+2x-7x-14\)

\(=x\left(x+2\right)-7\left(x+2\right)\)

\(=\left(x+2\right)\left(x-7\right)\)

Bài 3

Áp dụng tính chất dãy tỉ số bằng nhau,ta có:
\(\frac{y+z+1}{x}=\frac{x+z+2}{y}=\frac{x+y-3}{z}=\frac{y+z+1+x+y+2+x+y-3}{x+y+z}=\frac{2\left(x+y+z\right)}{x+y+z}=2\)
=> 1/(x+y+z) = 2
<=> x + y + z = 1/2 <=> y + z = 1/2 - x (1)
.(y+z+1)/x = 2 <=> y + z + 1 = 2x
kết hợp với (1) => 1/2 - x + 1 = 2x
<=> x = 1/2 => y + z = 0 <=> y = -z
có (x+y-3)/z = 2
<=> x + y - 3 = 2z
<=> y - 2z = 5/2
do y = -z => -3z = 5/2 <=> z = -5/6
y = 5/6
Vậy nghiệm tìm được (x;y;z) = (1/2;5/6;-5/6)

a) (3x-7)⁵=32

=> (3x-7)⁵=2⁵

=> 3x-7=2

=> 3x=2+7=9

=>x=9:3=3

b) (4x-1)³=27.125

=> (4x-1)³=3³.5³

=> (4x-1)³=(3.5)³

=> (4x-1)³=15³

=> 4x-1=15

(Các bước còn lại tương tự câu a)

a)(3x-7)^5=32

(3x-7)^5=2^5

3x-7=2

3x=2+7

3x=9

x=9:3

x=3

bạn viết thiếu đầu bài rồi

X=50,49