1. Решите уравнения, a) 2x=\frac{2}{3} b) 3x-9=4 c) 3+8=6x d) 5x=18-2x e) 4\frac{1}{2}x=3x+2 f) 5-7x+4x=4\frac{4}{7} g) 3(x-\frac{4}{19})=2 h) 2\frac{1}{6}(x-8)=x-4,5 i) 4x-\frac{4}{9}=\frac{5}{6}+2x j) 3\frac{3}{7}(\frac{9}{4}x-\frac{7}{12})=\frac{5}{42} k) 15(x-2)=45\frac{60}{91}

Ответ:

Решение уравнений:

a)

2x = \frac{2}{3}

x = \frac{2}{3} \div 2

x = \frac{2}{3} \cdot \frac{1}{2}

x = \frac{1}{3}

b)

3x - 9 = 4

3x = 4 + 9

3x = 13

x = \frac{13}{3}

x = 4\frac{1}{3}

c)

3 + 8 = 6x

6x = 11

x = \frac{11}{6}

x = 1\frac{5}{6}

d)

5x = 18 - 2x

5x + 2x = 18

7x = 18

x = \frac{18}{7}

x = 2\frac{4}{7}

e)

4\frac{1}{2}x = 3x + 2

\frac{9}{2}x - 3x = 2

\frac{9}{2}x - \frac{6}{2}x = 2

\frac{3}{2}x = 2

x = 2 \div \frac{3}{2}

x = 2 \cdot \frac{2}{3}

x = \frac{4}{3}

x = 1\frac{1}{3}

f)

5 - 7x + 4x = 4\frac{4}{7}

5 - 3x = \frac{32}{7}

-3x = \frac{32}{7} - 5

-3x = \frac{32}{7} - \frac{35}{7}

-3x = -\frac{3}{7}

x = \frac{3}{7} \div 3

x = \frac{3}{7} \cdot \frac{1}{3}

x = \frac{1}{7}

g)

3(x - \frac{4}{19}) = 2

3x - \frac{12}{19} = 2

3x = 2 + \frac{12}{19}

3x = \frac{38}{19} + \frac{12}{19}

3x = \frac{50}{19}

x = \frac{50}{19} \div 3

x = \frac{50}{19} \cdot \frac{1}{3}

x = \frac{50}{57}

h)

2\frac{1}{6}(x - 8) = x - 4,5

\frac{13}{6}(x - 8) = x - \frac{9}{2}

\frac{13}{6}x - \frac{104}{6} = x - \frac{9}{2}

\frac{13}{6}x - \frac{52}{3} = x - \frac{9}{2}

\frac{13}{6}x - x = \frac{52}{3} - \frac{9}{2}

\frac{13}{6}x - \frac{6}{6}x = \frac{104}{6} - \frac{27}{6}

\frac{7}{6}x = \frac{77}{6}

x = \frac{77}{6} \div \frac{7}{6}

x = \frac{77}{6} \cdot \frac{6}{7}

x = 11

i)

4x - \frac{4}{9} = \frac{5}{6} + 2x

4x - 2x = \frac{5}{6} + \frac{4}{9}

2x = \frac{15}{18} + \frac{8}{18}

2x = \frac{23}{18}

x = \frac{23}{18} \div 2

x = \frac{23}{18} \cdot \frac{1}{2}

x = \frac{23}{36}

j)

3\frac{3}{7}(\frac{9}{4}x - \frac{7}{12}) = \frac{5}{42}

\frac{24}{7}(\frac{9}{4}x - \frac{7}{12}) = \frac{5}{42}

\frac{216}{28}x - \frac{168}{84} = \frac{5}{42}

\frac{54}{7}x - 2 = \frac{5}{42}

\frac{54}{7}x = \frac{5}{42} + 2

\frac{54}{7}x = \frac{5}{42} + \frac{84}{42}

\frac{54}{7}x = \frac{89}{42}

x = \frac{89}{42} \div \frac{54}{7}

x = \frac{89}{42} \cdot \frac{7}{54}

x = \frac{89}{6 \cdot 54}

x = \frac{89}{324}

k)

15(x - 2) = 45\frac{60}{91}

15x - 30 = \frac{4155}{91}

15x = \frac{4155}{91} + 30

15x = \frac{4155}{91} + \frac{2730}{91}

15x = \frac{6885}{91}

x = \frac{6885}{91} \div 15

x = \frac{6885}{91} \cdot \frac{1}{15}

x = \frac{459}{91}

x = 5\frac{4}{91}

Ответ: a) x = \frac{1}{3}; b) x = 4\frac{1}{3}; c) x = 1\frac{5}{6}; d) x = 2\frac{4}{7}; e) x = 1\frac{1}{3}; f) x = \frac{1}{7}; g) x = \frac{50}{57}; h) x = 11; i) x = \frac{23}{36}; j) x = \frac{89}{324}; k) x = 5\frac{4}{91}

Ответ: a) x = \frac{1}{3}; b) x = 4\frac{1}{3}; c) x = 1\frac{5}{6}; d) x = 2\frac{4}{7}; e) x = 1\frac{1}{3}; f) x = \frac{1}{7}; g) x = \frac{50}{57}; h) x = 11; i) x = \frac{23}{36}; j) x = \frac{89}{324}; k) x = 5\frac{4}{91}

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