a) Ta có: \(7-\left(2x+4\right)=-\left(x+4\right)\)

\(\Leftrightarrow7-2x-4=-x-4\)

\(\Leftrightarrow-2x+3+x+4=0\)

\(\Leftrightarrow-x+7=0\)

\(\Leftrightarrow-x=-7\)

hay x=7

Vậy: S={7}

b) Ta có: \(\dfrac{2+x}{5}-0.5x=\dfrac{1-2x}{4}+0.25\)

\(\Leftrightarrow\dfrac{4\left(2+x\right)}{20}-\dfrac{0.5x\cdot20}{20}=\dfrac{5\left(1-2x\right)}{20}+\dfrac{20\cdot0.25}{20}\)

\(\Leftrightarrow4\left(2+x\right)-10x=5\left(1-2x\right)+5\)

\(\Leftrightarrow8+4x-10x=5-10x+5\)

\(\Leftrightarrow-6x+8=-10x+10\)

\(\Leftrightarrow-6x+8+10x-10=0\)

\(\Leftrightarrow4x-2=0\)

\(\Leftrightarrow4x=2\)

hay \(x=\dfrac{1}{2}\)

Vậy: \(S=\left\{\dfrac{1}{2}\right\}\)

d) Ta có: \(\dfrac{x-1}{59}+\dfrac{x-2}{58}+\dfrac{x-3}{57}=\dfrac{x-59}{1}+\dfrac{x-58}{2}+\dfrac{x-57}{3}\)

\(\Leftrightarrow\dfrac{x-1}{59}-1+\dfrac{x-2}{58}-1+\dfrac{x-3}{57}-1=\dfrac{x-59}{1}-1+\dfrac{x-58}{2}-1+\dfrac{x-57}{3}-1\)

\(\Leftrightarrow\dfrac{x-60}{59}+\dfrac{x-60}{58}+\dfrac{x-60}{57}=\dfrac{x-60}{1}+\dfrac{x-60}{2}+\dfrac{x-60}{3}\)

\(\Leftrightarrow\left(x-60\right)\left(\dfrac{1}{59}+\dfrac{1}{58}+\dfrac{1}{57}\right)-\left(x-60\right)\left(1+\dfrac{1}{2}+\dfrac{1}{3}\right)=0\)

\(\Leftrightarrow\left(x-60\right)\left(\dfrac{1}{59}+\dfrac{1}{58}+\dfrac{1}{57}-1-\dfrac{1}{2}-\dfrac{1}{3}\right)=0\)

mà \(\dfrac{1}{59}+\dfrac{1}{58}+\dfrac{1}{57}-1-\dfrac{1}{2}-\dfrac{1}{3}\ne0\)

nên x-60=0

hay x=60

Vậy: S={60}

M = 60 - 59 + 58 - 57 + 56 - 55 + ... + 4 - 3 + 2 - 1

M = ( 60 - 59 ) + ( 58 - 57 ) + ( 56 - 55 ) + ... + ( 4 - 3 ) + ( 2 - 1 )

M = 1 + 1 + 1 + ... + 1 + 1

Vì tổng M có 60 số hạng,mà 2 số hạng tạo thành 1 cặp nên 60 số hạng tạo thành 30 cặp

M = 1 . 30

M = 30

ta thấy: A= 10^m+2/10^m-1>10^m/10^m-1

mà B=10^m/10^m-3<10^m/10^m-1         (m thuộc N * ) ;

=> A<B

tương tự (phân số trung gian)

nhân 2 vế cho \(\frac{1}{2^3}\)

Ta có:

1+2+3-4-5-6+7+8+9-..........+55+56+57-58-59-60

=(1+2+3-4-5-6)+(7+8+9-10-11-12)..........+(55+56+57-58-59-60)

=  -3+ (-3)+...+(-3)

---12 số------------

=(-3).12

=-36

1711

cho xin vài tick nhé các bạn    Thanks

 Số các số hạng là:

(58 - 1) + 1 = 58 (số)

Tổng là:

(58 + 1) x 58 : 2 = 1711   

a) \(36.\left(-57\right)-57.64\)

\(=36.\left(-57\right)+\left(-57\right).64=\left(-57\right).\left(36+64\right)\)

\(=\left(-57\right).100=-5700\)

b)\(32.\left(-17\right)+\left(-18\right).17-50.13\)

\(=\left(-32\right).17+\left(-18\right).17-50.13\)

\(=17.\left(-32-18\right)-50.13=17.\left(-50\right)+\left(-50\right).13\)

\(=\left(-50\right).\left(17+13\right)=\left(-50\right).30=-150\)

c)\(-\left(-35\right)+12-|-35|-42\)

\(=35+12-35-42=12-42=-30\)

d)\(\left(-15-12\right):\left(-3\right)^2+5-13.\left(-2\right)+\left(-64\right):2^3\)

\(=-27:9+5+26-64:8=-3+5+26-8=20\)

e)\(\left(135-35\right).\left(-37\right)+37.\left(-42-58\right)=100.\left(-37\right)+37.\left(-100\right)\)

\(=\left(-100\right).37+37.\left(-100\right)=\left(-100\right).\left(37+37\right)\)

\(=\left(-100\right).74=-7400\)

Chúc em học tốt!!!!!!

Giải thích gõ mỏi tay lắm nên mình chỉ ghi đáp án thôi nha !!!

a)-5700

b)-1500

c)-30

d)20

d)-7400