Cho hình vẽ:

Hai tia \(Ax\) và \(By\) có vị trí như thế nào với nhau?

a) \[3,22 + 10,78 - 3,14\].

\[ = \left( {3,22 + 10,78} \right) - 3,14\]

\[ = 14 - 3,14\]

\[ = 10,86\].

c) \[20\%  - \frac{1}{2}:\frac{3}{4} + 0,2.\frac{{ - 2}}{3}\].

\[ = \frac{1}{5} - \frac{2}{3} + \frac{1}{5}.\frac{{ - 2}}{3}\]

\[ = \frac{1}{5} - \frac{2}{3} + \frac{{ - 2}}{{15}}\]

\[ = \frac{{ - 3}}{5}\].

b) \(\frac{2}{5} - \frac{1}{5}.\frac{3}{{ - 4}}\)

\( = \frac{2}{5} - \frac{3}{{ - 20}}\)

\( = \frac{8}{{20}} + \frac{3}{{20}}\)

\( = \frac{{11}}{{20}}\);

d) \[\frac{6}{{11}}.\frac{8}{{15}} + \frac{6}{{11}}.\frac{7}{{15}} + \frac{{ - 5}}{{11}}\]

\[ = \frac{6}{{11}}.\left( {\frac{8}{{15}} + \frac{7}{{15}}} \right) + \frac{{ - 5}}{{11}}\]

\[ = \frac{6}{{11}}.1 + \frac{{ - 5}}{{11}}\]

\[ = \frac{6}{{11}} + \frac{{ - 5}}{{11}}\]

\[ = \frac{1}{{11}}\].

a) \[x + 1,05 = 4,25 - 0,2\]

\[x + 1,05 = 4,05\]

\[x = 4,05 - 1,05\]

\[x = 3\].

Vậy \[x = 3\].

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

\(\frac{{5\left( {x - 7} \right)}}{{15}} = \frac{{ - 3}}{{15}}\)

\(5\left( {x - 7} \right) =  - 3\)

\(5x - 35 =  - 3\)

\(5x =  - 3 + 35\)

\(5x = 32\)

\(x = \frac{{32}}{5}\)

Vậy \(x = \frac{{32}}{5}\).

c) \(\frac{5}{6} + \left( {5x + \frac{3}{2}} \right):\frac{8}{{15}} = 2\frac{1}{{12}}\)

\(\left( {5x + \frac{3}{2}} \right):\frac{8}{{15}} = \frac{{25}}{{12}} - \frac{5}{6}\)

\(\left( {5x + \frac{3}{2}} \right):\frac{8}{{15}} = \frac{{15}}{{12}}\)

\(5x + \frac{3}{2} = \frac{5}{4}.\frac{8}{{15}}\)

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

\(5x = \frac{2}{3} - \frac{3}{2}\)

\(5x = \frac{{ - 5}}{6}\)

  \(x =  - \frac{1}{6}\)

Vậy \(x =  - \frac{1}{6}\).