a) \(\frac{2}{3}+\frac{1}{3}:x=\frac{3}{5}\)

\(\frac{1}{3}:x=\frac{3}{5}-\frac{2}{3}=\frac{9}{15}-\frac{10}{15}=\frac{-1}{15}\)

\(x=\frac{-1}{15}.\frac{1}{3}\)

\(x=\frac{-1}{45}\)

Vậy x = \(\frac{-1}{45}\)

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

\(\left|2x-1\right|=4-1=3\)

2x-1 = 3 ; -3

TH1: 2.x - 1 = 3

2.x = 3 + 1 = 4

x = 4 : 2 = 2

TH2: 2.x - 1 = -3

2.x = -3 + 1 = -2

x = -2 : 2 = -1

Vậy x \(\in\){ 2 ; -1 }

Ngại làm ấn máy ==

2. a, \(\dfrac{x}{9}=\dfrac{2}{3}\Leftrightarrow3x=2.9\)
<=> 3x = 18
<=> x = 6
@Hà Thái

2b) \(\left(2+3+4+...+2004\right).x=2016.2013\)

Ta có : Từ 2 đến 2004 có : 2004-2+1=2003 (số hạng)

\(\Rightarrow2+3+4+...+2004=\dfrac{\left(2+2004\right).2003}{2}=2009009\)

\(\Rightarrow2009009x=2016.2013\)

\(\Rightarrow x=\dfrac{2016.2013}{2009009}\approx2\)

1. a, \(\dfrac{6}{7}:\left(\dfrac{1}{2}.\dfrac{3}{4}\right)-\dfrac{5}{8}\)

= \(\dfrac{6}{7}:\dfrac{3}{8}-\dfrac{5}{8}\)

= \(\dfrac{16}{7}-\dfrac{5}{8}\)

= \(\dfrac{93}{56}\)
@Hà Thái

1.\(2x\left(x-3\right)-5\left(3-x\right)=0\)

\(\Leftrightarrow2x\left(x-3\right)+5\left(x-3\right)=0\)

\(\Leftrightarrow\left(2x+5\right)\left(x-3\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}2x+5=0\\x-3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{5}{2}\\x=3\end{matrix}\right.\)

2.\(B=x^2+4x+5\)

\(B=x^2+4x+4+1\)

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

Vì \(\left(x+2\right)^2\ge0\forall x\)

\(\Rightarrow\left(x+2\right)^2+1\ge1\)

\(\Rightarrow Min_B=1\) khi x+2=0\(\Rightarrow\)x=-2

bài 6:

\(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=x^2-3x+1\)

Bài 1:

\(f\left(x\right)=5x-3.\)

+ \(f\left(x\right)=0\)

\(\Rightarrow5x-3=0\)

\(\Rightarrow5x=0+3\)

\(\Rightarrow5x=3\)

\(\Rightarrow x=3:5\)

\(\Rightarrow x=\frac{3}{5}\)

Vậy \(x=\frac{3}{5}.\)

+ \(f\left(x\right)=1\)

\(\Rightarrow5x-3=1\)

\(\Rightarrow5x=1+3\)

\(\Rightarrow5x=4\)

\(\Rightarrow x=4:5\)

\(\Rightarrow x=\frac{4}{5}\)

Vậy \(x=\frac{4}{5}.\)

+ \(f\left(x\right)=-2010\)

\(\Rightarrow5x-3=-2010\)

\(\Rightarrow5x=\left(-2010\right)+3\)

\(\Rightarrow5x=-2007\)

\(\Rightarrow x=\left(-2007\right):5\)

\(\Rightarrow x=-\frac{2007}{5}\)

Vậy \(x=-\frac{2007}{5}.\)

Làm tương tự với \(f\left(x\right)=2011.\)

Chúc bạn học tốt!

Bài 3:

\(=\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\dfrac{1}{131}\)

\(=\dfrac{21+10+4}{35}+\dfrac{-9-2-7}{18}+\dfrac{1}{131}\)

=1/131

Bài 5:

a: Phần nguyên là 0

b: Phần nguyên là -1

Bài 1:

Tổng các chữ số của \(A\) là \(9n\)

\(A^2=99...9800...01\left(n-1\text{ chữ số }9\text{ và chữ số }0\right)\)

Vậy tổng các chữ số của \(A^2\) là \(\left(9+0\right)\left(n-1\right)+8+1=9\left(n-1\right)+9=9\left(n-1+1\right)=9n\)

Vậy tổng các chữ số của \(A\) bằng tổng các chữ số của \(A^2\) .

Bài 1:

a)

\(A=\dfrac{-5}{6}\cdot\dfrac{3}{10}\\ =\dfrac{\left(-5\right)\cdot3}{6\cdot10}\\ =\dfrac{-1}{4}\)

b)

\(B=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{12}\\ =\dfrac{4}{12}-\dfrac{3}{12}+\dfrac{1}{12}\\ =\dfrac{4-3+1}{12}\\ =\dfrac{1}{6}\)

Bài 2:

\(A=\left(\dfrac{-1}{5}\right)\cdot\dfrac{15}{4}+\left|\dfrac{4}{5}-\dfrac{14}{5}\right|:\dfrac{8}{3}\\ =\left(\dfrac{-1}{5}\right)\cdot\dfrac{15}{4}+\left|\dfrac{-10}{5}\right|\cdot\dfrac{3}{8}\\ =\left(\dfrac{-1}{5}\right)\cdot\dfrac{15}{4}+2\cdot\dfrac{3}{8}\\ =\dfrac{-3}{4}+\dfrac{3}{4}\\ =0\)

\(B=\left(\dfrac{-1}{2}\right)^2:1\dfrac{3}{8}+25\%\cdot\dfrac{3}{11}\\ =\left(\dfrac{-1}{2}\right)^2:\dfrac{11}{8}+\dfrac{3}{4}\cdot\dfrac{3}{11}\\ =\dfrac{1}{4}\cdot\dfrac{8}{11}+\dfrac{3}{4}\cdot\dfrac{3}{11}\\ =\dfrac{8}{44}+\dfrac{9}{44}\\ =\dfrac{17}{44}\)

\(C=\dfrac{-8}{5}+0,6+\left|\dfrac{-1}{2}\right|+\dfrac{1}{2}\\ =\dfrac{-8}{5}+\dfrac{3}{5}+\dfrac{1}{2}+\dfrac{1}{2}\\ =\left(\dfrac{-8}{5}+\dfrac{3}{8}\right)+\left(\dfrac{1}{2}+\dfrac{1}{2}\right)\\ =\left(-1\right)+1\\ =0\)

\(D=\dfrac{-5}{9}\cdot\dfrac{2}{13}+\dfrac{-5}{9}:\dfrac{13}{11}+1\dfrac{5}{9}\\ =\dfrac{-5}{9}\cdot\dfrac{2}{13}+\dfrac{-5}{9}\cdot\dfrac{11}{13}+\dfrac{14}{9}\\ =\dfrac{-5}{9}\cdot\left(\dfrac{2}{13}+\dfrac{11}{13}\right)+\dfrac{14}{9}\\ =\dfrac{-5}{9}\cdot1+\dfrac{14}{9}\\ =\dfrac{-5}{9}+\dfrac{14}{9}\\ =1\)

Bài 3:

a)

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

b)

\(\dfrac{3}{5}x+0,4x=2\\\dfrac{3}{5}x+\dfrac{2}{5}x=2\\ x\left(\dfrac{3}{5}+\dfrac{2}{5}\right)=2\\ x=2 \)

c)

\(\dfrac{x}{-3}=\dfrac{7}{6}+\left(\dfrac{-15}{18}\right)\\ \dfrac{-x}{3}=\dfrac{1}{3}\\ \Rightarrow-x=1\\ \Leftrightarrow x=-1\)

d)

\(\dfrac{4}{3}\cdot\left(\dfrac{1}{6}-\dfrac{1}{2}\right)< x< \dfrac{2}{3}\cdot\left(\dfrac{-1}{6}+\dfrac{3}{4}\right)\\ \Leftrightarrow\dfrac{4}{3}\cdot\dfrac{-1}{3}< x< \dfrac{2}{3}\cdot\dfrac{7}{12}\\ \Leftrightarrow\dfrac{-4}{9}< x< \dfrac{7}{18}\\ \Rightarrow x=0\)