\(5^7.5^5=5^{7+5}=5^{12}\)

\(2^{10}:64.16=2^{10}:2^6.2^4=2^{10-6+4}=2^8\)

\(9^5:8^0=9^5:1=9^5\)

\(x-2y+x^2-4y^2\)

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

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

\(=\left(x-2y\right)\left(x+2y+1\right)\)

1. more optimistically

2. popularly

3. less densely populated

4. more quickly

5. more easily

6. better

a) \(\dfrac{3}{5}\times x=\dfrac{4}{15}+\dfrac{7}{3}\)

\(\dfrac{3}{5}\times x=\dfrac{4}{15}+\dfrac{7\times5}{3\times5}\)

\(\dfrac{3}{5}\times x=\dfrac{4}{15}+\dfrac{35}{15}\)

\(\dfrac{3}{5}\times x=\dfrac{4+35}{15}\)

\(\dfrac{3}{5}\times x=\dfrac{39}{15}\)

\(\dfrac{3}{5}\times x=\dfrac{13}{5}\)

\(x=\dfrac{13}{5}:\dfrac{3}{5}\)

\(x=\dfrac{13}{5}\times\dfrac{5}{3}\)

\(x=\dfrac{13}{3}\)

b) \(x:\dfrac{3}{5}=\dfrac{7}{8}:\dfrac{10}{9}\)

\(x:\dfrac{3}{5}=\dfrac{7}{8}\times\dfrac{9}{10}\)

\(x:\dfrac{3}{5}=\dfrac{63}{80}\)

\(x=\dfrac{63}{80}\times\dfrac{3}{5}\)

\(x=\dfrac{189}{400}\)

1. better

2. faster

3. later

4. harder

5. worse

6. earlier

a. \(\dfrac{x-1}{27}=\dfrac{-1}{3}\)

\(\Rightarrow3\left(x-1\right)=27.\left(-1\right)\)

\(3x-3=-27\)

\(3x=-27+3\)

\(3x=-24\)

\(x=-24:3\)

\(x=-8\)

b. \(\dfrac{x-3}{-25}=\dfrac{-4}{x-3}\)

\(\Rightarrow\left(x-3\right)^2=\left(-25\right).\left(-4\right)\)

\(\left(x-3\right)^2=100\)

\(\left(x-3\right)^2=10^2\)

\(\Rightarrow x-3=10\) hoặc \(x-3=-10\)

\(\Rightarrow x=10+3\) hoặc \(x=-10+3\)

\(\Rightarrow x=13\) hoặc \(x=-7\)

1) Giải pt:

a, \(\sqrt{\left(3x-1\right)^2}=2\Leftrightarrow\left|3x-1\right|=2\Leftrightarrow\left[{}\begin{matrix}3x-1=2\\3x-1=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=3\\3x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)

Vậy phương trình có tập nghiệm là: \(S=\left\{1;-\dfrac{1}{3}\right\}.\)

b, \(\left(2x+10\right)\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}2x+10=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=4\end{matrix}\right.\)

Vậy phương trình có tập nghiệm là: \(S=\left\{-5;4\right\}.\)

2) Giải hệ pt:

a, \(\left\{{}\begin{matrix}2x-y=1-2y\\3x+y=3-x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+y=1\\4x+y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1-2x\\4x+\left(1-2x\right)=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1-2x\\2x=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-1\end{matrix}\right.\)

Vậy hệ phương trình có nghiệm là: \(\left(x;y\right)=\left(1;-1\right).\)

b, \(\left\{{}\begin{matrix}x-y=1\\3x+1=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y=1\\3x=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)

Vậy hệ phương trình có nghiệm là: \(\left(x;y\right)=\left(2;1\right).\)

a) \(x-68=-1256\)

\(x=-1256+68\)

\(x=-1188\)

b) \(3-\left(x+9\right)=67.\left(-2\right)\)

\(3-\left(x+9\right)=-134\)

\(x+9=3+134\)

\(x+9=137\)

\(x=137-9\)

\(x=128\)

c) \(2x+\left(-68\right)-\left(-3\right)=-2020\)

\(2x-68+3=-2020\)

\(2x-65=-2020\)

\(2x=-2020+65\)

\(2x=-1955\)

\(x=-1955:2\)

\(x=-977,5\)

d) \(x-\left(x-5\right)=0\)

\(x-5=x\)

\(x-x-5=0\)

\(-5=0\) (vô lí)

e) \(x^2-112=34\)

\(x^2=34+112\)

\(x^2=146\)

\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{146}\\x=-\sqrt{146}\end{matrix}\right.\)

g) \(\left(x-6\right)^3=-125\)

\(\left(x-6\right)^3=\left(-5\right)^3\)

\(\Rightarrow x-6=-5\)

\(x=-5+6\)

\(x=1\)

1. I'm meeting Andy at / on the cinema in an hour.
2. Have you seen the new building at / in front of the school?
3. My new job starts in / on the first day of August.
4. We're going to Martin's to see their new baby in / on Wednesday evening.
5. See if there are any tomatoes at / in the fridge, will you?
6. We'll all have computers connected to our brains at / in the future.
7. I don't feel like playing chess at / on the moment.
8. I think there's someone at / in the door. I'll go and check.

1. to

2. to

3. in

4. at

5. to

6. to

7. in

8. on

9. in

10. to