Đáp án:

Giải thích các bước giải:

Câu 5

$x - \frac{3}{10} = \frac{7}{15} \cdot \frac{3}{5}$

$<=>$$x - \frac{3}{10} = \frac{7}{25}$

$<=>$$x = \frac{7}{25} + \frac{3}{10} = \frac{14}{50} + \frac{15}{50}$

$<=>$$x = \frac{29}{50}$

Câu 6

$x + \frac{1}{3} = \frac{-7}{26} \cdot \frac{13}{6}$

$<=>$$x + \frac{1}{3} = \frac{-7}{12}$

$<=>$$x = \frac{-7}{12} - \frac{1}{3} = \frac{-7}{12} - \frac{4}{12}$

$<=>$$x = \frac{-11}{12}$

Câu 7

$\frac{1}{2} - \frac{1}{2} : x = \frac{3}{4}$

$<=>$$\frac{1}{2} : x = \frac{1}{2} - \frac{3}{4} = \frac{2}{4} - \frac{3}{4}$

$<=>$$\frac{1}{2} : x = \frac{-1}{4}$

$<=>$$x = \frac{1}{2} : \left( \frac{-1}{4} \right) = \frac{1}{2} \cdot (-4)$

$<=>$$x = -2$

Câu 8

$\frac{7}{5} + \frac{2}{5} : x = 2$

$<=>$$\frac{2}{5} : x = 2 - \frac{7}{5} = \frac{3}{5}$

$<=>$$x = \frac{2}{5} : \frac{3}{5} = \frac{2}{3}$

Câu 9

$\frac{5}{12} + \frac{-7}{12} : x = \frac{-3}{10}$

$<=>$$\frac{-7}{12} : x = \frac{-3}{10} - \frac{5}{12} = \frac{-18}{60} - \frac{25}{60}$

$<=>$$\frac{-7}{12} : x = \frac{-43}{60}$

$<=>$$x = \frac{-7}{12} \cdot \left( \frac{-60}{43} \right) = \frac{35}{43}$

Câu 10

$5\frac{3}{5}x - \frac{1}{3} = \frac{4}{3}$

$<=>$$\frac{28}{5}x = \frac{4}{3} + \frac{1}{3} = \frac{5}{3}$

$<=>$$x = \frac{5}{3} : \frac{28}{5} = \frac{5}{3} \cdot \frac{5}{28}$

$<=>$$x = \frac{25}{84}$

Câu 11

$\frac{3}{4} + \frac{1}{4} \cdot x = \frac{5}{8}$

$<=>$$\frac{1}{4} \cdot x = \frac{5}{8} - \frac{3}{4} = \frac{5}{8} - \frac{6}{8}$

$<=>$$\frac{1}{4} \cdot x = \frac{-1}{8}$

$<=>$$x = \frac{-1}{8} \cdot 4 = \frac{-1}{2}$

Câu 12

$2\frac{7}{2} - \frac{11}{5}x = \frac{1}{5}$

$<=>$$\frac{11}{5}x = \frac{11}{2} - \frac{1}{5} = \frac{55}{10} - \frac{2}{10} = \frac{53}{10}$

$<=>$$x = \frac{53}{10} \cdot \frac{5}{11} = \frac{53}{22}$

Câu 13

$\frac{4}{7}x - \frac{3}{4} = \frac{-5}{6}$

$<=>$$\frac{4}{7}x = \frac{-5}{6} + \frac{3}{4} = \frac{-10}{12} + \frac{9}{12} = \frac{-1}{12}$

$<=>$$x = \frac{-1}{12} \cdot \frac{7}{4} = \frac{-7}{48}$

Câu 14

$\frac{1}{3} + \frac{1}{2} : x = \frac{-5}{6}$

$<=>$$\frac{1}{2} : x = \frac{-5}{6} - \frac{1}{3} = \frac{-5}{6} - \frac{2}{6} = \frac{-7}{6}$

$<=>$$x = \frac{1}{2} \cdot \left( \frac{-6}{7} \right) = \frac{-3}{7}$

Câu 15

$\frac{2}{3} + \frac{1}{3} : x = 75\%$

$<=>$$\frac{1}{3} : x = \frac{3}{4} - \frac{2}{3} = \frac{9}{12} - \frac{8}{12} = \frac{1}{12}$

$<=>$$x = \frac{1}{3} \cdot 12 = 4$

Câu 16

$\left( 2\frac{4}{5}x - 50 \right) : \frac{2}{3} = 51$

$<=>$$\frac{14}{5}x - 50 = 51 \cdot \frac{2}{3} = 34$

$<=>$$\frac{14}{5}x = 84 \Rightarrow x = 84 \cdot \frac{5}{14} = 30$

Câu 17

$(x - 0,5)^2 - \frac{3}{10} = 1,14$

$<=>$$(x - 0,5)^2 = 1,44 = (1,2)^2$

TH1: $x - 0,5 = 1,2 \Rightarrow x = 1,7$

TH2: $x - 0,5 = -1,2 \Rightarrow x = -0,7$

Câu 18

$7,75 - 3x = 1,75$

$<=>$$3x = 7,75 - 1,75 = 6$

$<=>$$x = 2$

Câu 19

$60\%x + \frac{2}{3}x = -76$

$<=>$$\left( \frac{3}{5} + \frac{2}{3} \right)x = -76 \Rightarrow \frac{19}{15}x = -76$

$<=>$$x = -76 \cdot \frac{15}{19} = -60$

Câu 20

$\frac{-5}{6} - x = \frac{7}{12} + \frac{-1}{3}$

$<=>$$\frac{-5}{6} - x = \frac{7}{12} - \frac{4}{12} = \frac{3}{12} = \frac{1}{4}$

$<=>$$x = \frac{-5}{6} - \frac{1}{4} = \frac{-10}{12} - \frac{3}{12} = \frac{-13}{12}$

Câu 21

$x - 4 = \frac{-14}{35} : \frac{7}{5}$

$<=>$$x - 4 = \frac{-2}{5} \cdot \frac{5}{7} = \frac{-2}{7}$

$<=>$$x = 4 - \frac{2}{7} = \frac{28}{7} - \frac{2}{7} = \frac{26}{7}$

Bổ sung :

Câu 5) $3,21 \cdot \left( \frac{1}{2} - 2,5 \right) + 28,08 : (-1,3)$

$= 3,21 \cdot (-2) + (-21,6)$

$= -6,42 - 21,6 = -28,02$

Câu 6) $-1,25 \cdot \left( \frac{3}{2} - 0,75 \right) + 3,5 : (-1,4)$

$= -1,25 \cdot 0,75 + (-2,5)$

$= -0,9375 - 2,5 = -3,4375$