[BT-T7-1.2#4] Bài tập TÌM $x$ (số hữu tỷ)

Sau đây là các bài tập TOÁN về TÌM $x$ (số hữu tỷ) dành cho học sinh lớp 7. Trước khi làm bài tập, nên xem lại lý thuyết trong các bài liên quan:

Các dạng bài tập thường gặp:

Bài tập 1: Tìm $x,$ biết:

a) $x + \dfrac{1}{5} = \dfrac{3}{7};$

b) $x – \dfrac{3}{4} = \dfrac{1}{2};$

c) $\dfrac{2}{3} – x = \dfrac{7}{5}.$

Bài tập 2: Tìm $x,$ biết:

a) $x-\dfrac{2}{3} = \dfrac{7}{2} – \dfrac{11}{6};$

b) $x + \dfrac{4}{5} = \dfrac{5}{6} + \dfrac{7}{10};$

c) $\dfrac{1}{2} + x = \dfrac{-3}{2} – \dfrac{1}{5};$

d) $\dfrac{2}{5} – x = \dfrac{2}{5} + \dfrac{2}{3}.$

Bài tập 3: Tìm $x,$ biết:

a) $x + \dfrac{1}{7} = 3 – 1\dfrac{1}{2};$

b) $x + \dfrac{2}{9} = 1\dfrac{1}{2} – \dfrac{7}{9};$

c) $\dfrac{16}{5} – x = \dfrac{4}{5} – \dfrac{3}{10};$

d) $\dfrac{1}{3} – x = \dfrac{5}{6} – \dfrac{1}{4}.$

Bài tập 4: Tìm $x,$ biết:

a) $0,5 + x = \dfrac{2}{5};$

b) $1,75 + x = \dfrac{3}{2} – 0,9;$

c) $x – 1\dfrac{1}{2} = 2,7 + 6,3;$

d) $\dfrac{6}{15} – x = \dfrac{-7}{2} + 1,11.$

Bài tập 5: Tìm $x:$

a) $x+\dfrac{1}{4} = \dfrac{2}{5} – \left(-\dfrac{1}{4}\right);$

b) $x + \dfrac{5}{9} = \dfrac{-7}{13} – \left(\dfrac{-5}{9}\right);$

c) $\dfrac{1}{20} – \left(x – \dfrac{8}{5}\right) = \dfrac{1}{10};$

d) $\dfrac{-3}{11} – \left(x – \dfrac{2}{5}\right) = -\dfrac{14}{22}.$

Bài tập 6: Tìm $x:$

a) $\dfrac{3}{4} + 2x = \dfrac{1}{8};$

b) $\dfrac{7}{9} – 3x = \dfrac{-5}{3};$

c) $7x + \dfrac{11}{9} = \dfrac{4}{3} – 0,5.$

Bài tập 7: Tìm $x,$ biết:

a) $\dfrac{7}{2} – \left[ \dfrac{3}{2} – \left( x + \dfrac{7}{2}\right)\right] = \dfrac{-9}{11};$

b) $x – \left[\dfrac{5}{3} – \left(-\dfrac{7}{2}+ \dfrac{4}{5}\right)\right] = \dfrac{-1}{5};$

c) $1 – \left(-x + \dfrac{9}{5}\right) = \dfrac{5}{6} + \left(-\dfrac{7}{12}\right);$

d) $1 – \left(\dfrac{8}{7} – x\right) = \dfrac{4}{5} + \dfrac{-1}{10}.$

Bài tập 8: Tìm $x,$ biết:

a) $\dfrac{x}{15} – \dfrac{3}{5} = \dfrac{-2}{3};$

b) $\dfrac{5}{6} – \dfrac{x}{5} = \dfrac{19}{30};$

c) $\dfrac{11}{8} – \dfrac{85}{x} = \dfrac{-13}{6}.$

Bài tập 9: Tìm $x:$

a) $x : \dfrac{5}{7} = -\dfrac{21}{20};$

b) $\dfrac{4}{5} : x = \dfrac{-7}{20};$

c) $\dfrac{4}{5}\cdot x = \dfrac{-4}{15};$

d) $x\cdot \dfrac{-7}{15} = -\dfrac{21}{45}.$

Bài tập 10: Tìm $x:$

a) $\dfrac{2}{5}x + \dfrac{5}{7} = \dfrac{3}{10};$

b) $\dfrac{3}{4}x – \dfrac{1}{2} = \dfrac{3}{7};$

c) $\dfrac{-2}{5} +\dfrac{5}{6}x = \dfrac{-4}{15};$

d) $(-0,2) – \dfrac{1}{6}x = \dfrac{2}{3}.$

Bài tập 11: Tìm $x:$

a) $x : \dfrac{1}{2} = \dfrac{-2}{3} – \dfrac{2}{5};$

b) $\dfrac{-4}{5} – x : \dfrac{1}{3} = \dfrac{1}{2};$

c) $\dfrac{4}{3} + \dfrac{5}{8} : x = \dfrac{1}{12};$

d) $\left(-0,75x + \dfrac{5}{2}\right)\cdot \dfrac{4}{7} = \dfrac{-1}{3}.$

Đáp án các bài tập:

Bài tập 1:

a) $x + \dfrac{1}{5} = \dfrac{3}{7}$

$x = \dfrac{3}{7} – \dfrac{1}{5}$

$x = \dfrac{15}{35} – \dfrac{7}{35}$

$x = \dfrac{8}{35}.$

b) $x – \dfrac{3}{4} = \dfrac{1}{2}$

$x = \dfrac{1}{2} + \dfrac{3}{4}$

$x = \dfrac{2}{4} + \dfrac{3}{4}$

$x = \dfrac{5}{4}.$

c) $\dfrac{2}{3} – x = \dfrac{7}{5}$

$\dfrac{2}{3} – \dfrac{7}{5} = x$

$x = \dfrac{2}{3} – \dfrac{7}{5}$

$x = \dfrac{10}{15} – \dfrac{21}{15}$

$x = \dfrac{-11}{15}.$

Bài tập 2:

a) $x-\dfrac{2}{3} = \dfrac{7}{2} – \dfrac{11}{6}$

$x = \dfrac{7}{2} – \dfrac{11}{6} + \dfrac{2}{3}$

$x = \dfrac{21}{6} – \dfrac{11}{6} + \dfrac{4}{6}$

$x = \dfrac{14}{6}$

$x = \dfrac{7}{3}.$

b) $x + \dfrac{4}{5} = \dfrac{5}{6} + \dfrac{7}{10}$

$x = \dfrac{5}{6} + \dfrac{7}{10} – \dfrac{4}{5}$

$x = \dfrac{25}{30} + \dfrac{21}{30} – \dfrac{24}{30}$

$x = \dfrac{22}{30}$

$x = \dfrac{11}{15}.$

c) $\dfrac{1}{2} + x = \dfrac{-3}{2} – \dfrac{1}{5}$

$x = \dfrac{-3}{2} – \dfrac{1}{5} – \dfrac{1}{2}$

$x = \dfrac{-3}{2} – \dfrac{1}{2} – \dfrac{1}{5}$

$x = \dfrac{-4}{2} – \dfrac{1}{5}$

$x = -2 – \dfrac{1}{5}$

$x = -\left(2+ \dfrac{1}{5}\right)$

$x = -2\dfrac{1}{5}.$

d) $\dfrac{2}{5} – x = \dfrac{2}{5} + \dfrac{2}{3}$

$\dfrac{2}{5} – \dfrac{2}{5} – \dfrac{2}{3} = x$

$x = \dfrac{2}{5} – \dfrac{2}{5} – \dfrac{2}{3}$

$x = -\dfrac{2}{3}.$

Bài tập 3:

a) $x + \dfrac{1}{7} = 3 – 1\dfrac{1}{2}$

$x = 3 – 1\dfrac{1}{2} – \dfrac{1}{7}$

$x = 3 – \dfrac{3}{2} – \dfrac{1}{7}$

$x = \dfrac{42}{14} – \dfrac{21}{14} – \dfrac{2}{14}$

$x = \dfrac{19}{14}.$

b) $x + \dfrac{2}{9} = 1\dfrac{1}{2} – \dfrac{7}{9}$

$x = 1\dfrac{1}{2} – \dfrac{7}{9} – \dfrac{2}{9}$

$x = \dfrac{3}{2} – \left(\dfrac{7}{9} + \dfrac{2}{9}\right)$

$x = \dfrac{3}{2} – \dfrac{9}{9}$

$x = \dfrac{3}{2} – 1$

$x = \dfrac{1}{2}.$

c) $\dfrac{16}{5} – x = \dfrac{4}{5} – \dfrac{3}{10}$

$\dfrac{16}{5} – \dfrac{4}{5} + \dfrac{3}{10} = x$

$x = \dfrac{16}{5} – \dfrac{4}{5} + \dfrac{3}{10}$

$x = \dfrac{12}{5} + \dfrac{3}{10}$

$x = \dfrac{24}{10} + \dfrac{3}{10}$

$x = \dfrac{27}{10} = 2,7.$

d) $\dfrac{1}{3} – x = \dfrac{5}{6} – \dfrac{1}{4}$

$x = \dfrac{1}{3} – \dfrac{5}{6} + \dfrac{1}{4}$

$x = \dfrac{4}{12} – \dfrac{10}{12} + \dfrac{3}{12}$

$x = \dfrac{-3}{12}$

$x = \dfrac{-1}{4}.$

Bài tập 4:

a) $0,5 + x = \dfrac{2}{5}$

$0,5 + x = 0,4$

$x = 0,4 – 0,5$

$x = -0,1.$

b) $1,75 + x = \dfrac{3}{2} – 0,9$

$1,75+x = 1,5 – 0,9$

$x = 1,5 – 0,9 – 1,75$

$x = -1,15.$

c) $x – 1\dfrac{1}{2} = 2,7 + 6,3$

$x = 2,7 + 6,3 + 1\dfrac{1}{2}$

$x = 2,7 + 6,3 + 1 + \dfrac{1}{2}$

$x = 2,7 + 6,3 + 1 + 0,5$

$x = 10,5.$

d) $\dfrac{6}{15} – x = \dfrac{-7}{2} + 1,11$

$x = \dfrac{6}{15} – \dfrac{-7}{2} – 1,11$

$x = \dfrac{2}{5} + \dfrac{7}{2} – 1,11$

$x = 0,4 + 3,5 – 1,11$

$x = 2,79.$

Bài tập 5:

a) $x+\dfrac{1}{4} = \dfrac{2}{5} – \left(-\dfrac{1}{4}\right)$

$x + \dfrac{1}{4} = \dfrac{2}{5} + \dfrac{1}{4}$

$x = \dfrac{2}{5} + \dfrac{1}{4} – \dfrac{1}{4}$

$x = \dfrac{2}{5}.$

b) $x + \dfrac{5}{9} = \dfrac{-7}{13} – \left(\dfrac{-5}{9}\right)$

$x + \dfrac{5}{9} = \dfrac{-7}{13} + \dfrac{5}{9}$

$x = \dfrac{-7}{13} + \dfrac{5}{9} – \dfrac{5}{9}$

$x = \dfrac{-7}{13}.$

c) $\dfrac{1}{20} – \left(x – \dfrac{8}{5}\right) = \dfrac{1}{10}$

$x – \dfrac{8}{5} = \dfrac{1}{20} – \dfrac{1}{10}$

$x – \dfrac{8}{5} = \dfrac{1}{20} – \dfrac{2}{20}$

$x – \dfrac{8}{5} = \dfrac{-1}{20}$

$x = \dfrac{-1}{20} + \dfrac{8}{5}$

$x = \dfrac{-1}{20} + \dfrac{32}{20}$

$x = \dfrac{31}{20}.$

d) $\dfrac{-3}{11} – \left(x – \dfrac{2}{5}\right) = -\dfrac{14}{22}$

$\dfrac{-3}{11} + \dfrac{14}{22} = x-\dfrac{2}{5}$

$\dfrac{-3}{11} + \dfrac{14}{22} + \dfrac{2}{5} = x$

$x = \dfrac{-3}{11} + \dfrac{14}{22} + \dfrac{2}{5}$

$x = \dfrac{-3}{11} + \dfrac{7}{11} + \dfrac{2}{5}$

$x = \dfrac{4}{11} + \dfrac{2}{5}$

$x = \dfrac{20}{55} + \dfrac{22}{55}$

$x = \dfrac{42}{55}.$

Bài tập 6:

a) $\dfrac{3}{4} + 2x = \dfrac{1}{8}$

$2x = \dfrac{1}{8} – \dfrac{3}{4}$

$2x = \dfrac{1}{8} – \dfrac{6}{8}$

$2x = \dfrac{-5}{8}$

$x = \dfrac{-5}{8} : 2$

$x = \dfrac{-5}{16}.$

b) $\dfrac{7}{9} – 3x = \dfrac{-5}{3}$

$3x = \dfrac{7}{9} – \dfrac{-5}{3}$

$3x = \dfrac{7}{9} + \dfrac{5}{3}$

$3x = \dfrac{7}{9} + \dfrac{15}{9}$

$3x = \dfrac{22}{9}$

$x = \dfrac{22}{9} : 3$

$x = \dfrac{22}{27}.$

c) $7x + \dfrac{11}{9} = \dfrac{4}{3} – 0,5$

$7x = \dfrac{4}{3} – 0,5 – \dfrac{11}{9}$

$7x = \dfrac{12}{9} – 0,5 – \dfrac{11}{9}$

$7x = \dfrac{12}{9} – \dfrac{11}{9} – 0,5$

$7x = \dfrac{1}{9} – \dfrac{1}{2}$

$7x = \dfrac{2}{18} – \dfrac{9}{18}$

$7x = \dfrac{-7}{18}$

$x = \dfrac{-7}{18} : 7$

$x = \dfrac{-1}{18}.$

Bài tập 7:

a) $\dfrac{7}{2} – \left[ \dfrac{3}{2} – \left( x + \dfrac{7}{2}\right)\right] = \dfrac{-9}{11}$

$\dfrac{3}{2} – \left(x + \dfrac{7}{2}\right) = \dfrac{7}{2} + \dfrac{9}{11}$

$x + \dfrac{7}{2} = \dfrac{3}{2} – \dfrac{7}{2} – \dfrac{9}{11}$

$x = \dfrac{3}{2} – \dfrac{7}{2} – \dfrac{9}{11} – \dfrac{7}{2}$

$x = \dfrac{3}{2} – \dfrac{7}{2} – \dfrac{7}{2} – \dfrac{9}{11}$

$x = \dfrac{-11}{2} – \dfrac{9}{11}$

$x = \dfrac{-121}{22} – \dfrac{18}{22}$

$x = \dfrac{-139}{22}.$

b) $x – \left[\dfrac{5}{3} – \left(-\dfrac{7}{2}+ \dfrac{4}{5}\right)\right] = \dfrac{-1}{5}$

$x = \dfrac{-1}{5} + \left[\dfrac{5}{3} – \left(-\dfrac{7}{2}+ \dfrac{4}{5}\right)\right] $

$x = \dfrac{-1}{5} + \dfrac{5}{3} – \left(-\dfrac{7}{2} + \dfrac{4}{5}\right)$

$x = \dfrac{-1}{5} + \dfrac{5}{3} + \dfrac{7}{2} – \dfrac{4}{5}$

$x = \dfrac{-1}{5} – \dfrac{4}{5} + \dfrac{5}{3} + \dfrac{7}{2}$

$x = \dfrac{-5}{5} + \dfrac{5}{3} + \dfrac{7}{2}$

$x = -1 + \dfrac{5}{3} + \dfrac{7}{2}$

$x = \dfrac{-6}{6} + \dfrac{10}{6} + \dfrac{21}{6}$

$x = \dfrac{25}{6}.$

c) $1 – \left(-x + \dfrac{9}{5}\right) = \dfrac{5}{6} + \left(-\dfrac{7}{12}\right)$

$1 + x – \dfrac{9}{5} = \dfrac{5}{6} – \dfrac{7}{12}$

$x = \dfrac{5}{6} – \dfrac{7}{12} – 1 + \dfrac{9}{5}$

$x = \dfrac{10}{12} – \dfrac{7}{12} – 1 + \dfrac{9}{5}$

$x = \dfrac{3}{12} – 1 + \dfrac{9}{5}$

$x = \dfrac{1}{4} – 1 + \dfrac{9}{5}$

$x = \dfrac{5}{20} – \dfrac{20}{20} + \dfrac{36}{20}$

$x = \dfrac{21}{20}.$

d) $1 – \left(\dfrac{8}{7} – x\right) = \dfrac{4}{5} + \dfrac{-1}{10}$

$1 – \dfrac{8}{7} + x = \dfrac{4}{5} – \dfrac{1}{10}$

$x = \dfrac{4}{5} – \dfrac{1}{10} – 1 + \dfrac{8}{7}$

$x = \dfrac{8}{10} – \dfrac{1}{10} – 1 + \dfrac{8}{7}$

$x = \dfrac{7}{10} – 1 + \dfrac{8}{7}$

$x = \dfrac{49}{70} – \dfrac{70}{70} + \dfrac{80}{70}$

$x = \dfrac{59}{70}.$

Bài tập 8:

a) $\dfrac{x}{15} – \dfrac{3}{5} = \dfrac{-2}{3}$

$\dfrac{x}{15} = \dfrac{-2}{3} + \dfrac{3}{5}$

$\dfrac{x}{15} = \dfrac{-10}{15} + \dfrac{9}{15}$

$\dfrac{x}{15} = \dfrac{-1}{15}$

Do đó, $x = -1.$

b) $\dfrac{5}{6} – \dfrac{x}{5} = \dfrac{19}{30}$

$\dfrac{x}{5} = \dfrac{5}{6} – \dfrac{19}{30}$

$\dfrac{x}{5} = \dfrac{25}{30} – \dfrac{19}{30}$

$\dfrac{x}{5} = \dfrac{6}{30}$

$\dfrac{x}{5} = \dfrac{1}{5}$

Vậy $x = 1.$

c) $\dfrac{11}{8} – \dfrac{85}{x} = \dfrac{-13}{6}$

$\dfrac{85}{x} = \dfrac{11}{8} + \dfrac{13}{6}$

$\dfrac{85}{x} = \dfrac{33}{24} + \dfrac{52}{24}$

$\dfrac{85}{x} = \dfrac{85}{24}$

Vậy $x = 24.$

Bài tập 9:

a) $x : \dfrac{5}{7} = -\dfrac{21}{20}$

$x = -\dfrac{21}{20}\cdot \dfrac{5}{7}$

$x = -\dfrac{3}{4}.$

b) $\dfrac{4}{5} : x = \dfrac{-7}{20}$

$x = \dfrac{4}{5} : \dfrac{-7}{20}$

$x = \dfrac{4}{5} \cdot \dfrac{-20}{7}$

$x = \dfrac{4\cdot (-4)}{7}$

$x = \dfrac{-16}{7}.$

c) $\dfrac{4}{5}\cdot x = \dfrac{-4}{15}$

$x = \dfrac{-4}{15} : \dfrac{4}{5}$

$x = \dfrac{-4}{15} \cdot \dfrac{5}{4}$

$x = \dfrac{-1}{3}.$

d) $x\cdot \dfrac{-7}{15} = -\dfrac{21}{45}$

$x = -\dfrac{21}{45} : \dfrac{-7}{15}$

$x = -\dfrac{21}{45} \cdot \dfrac{-15}{7}$

$x = 1.$

Bài tập 10:

a) $\dfrac{2}{5}x + \dfrac{5}{7} = \dfrac{3}{10}$

$\dfrac{2}{5}x = \dfrac{3}{10} – \dfrac{5}{7}$

$\dfrac{2}{5}x = \dfrac{21}{70} – \dfrac{50}{70}$

$\dfrac{2}{5}x = \dfrac{-29}{70}$

$x = \dfrac{-29}{70} : \dfrac{2}{5}$

$x = \dfrac{-29}{70}\cdot \dfrac{5}{2}$

$x = \dfrac{-145}{140}.$

b) $\dfrac{3}{4}x – \dfrac{1}{2} = \dfrac{3}{7}$

$\dfrac{3}{4}x = \dfrac{3}{7} + \dfrac{1}{2}$

$\dfrac{3}{4}x = \dfrac{6}{14} + \dfrac{7}{14}$

$\dfrac{3}{4}x = \dfrac{13}{14}$

$x = \dfrac{13}{14} : \dfrac{3}{4}$

$x = \dfrac{13}{14}\cdot \dfrac{4}{3}$

$x = \dfrac{13\cdot 2}{7\cdot 3}$

$x = \dfrac{26}{21}.$

c) $\dfrac{-2}{5} +\dfrac{5}{6}x = \dfrac{-4}{15}$

$\dfrac{5}{6}x = \dfrac{-4}{15} + \dfrac{2}{5}$

$\dfrac{5}{6}x = \dfrac{-4}{15} + \dfrac{6}{15}$

$\dfrac{5}{6}x = \dfrac{2}{15}$

$x = \dfrac{2}{15}:\dfrac{5}{6}$

$x = \dfrac{2}{15}\cdot \dfrac{6}{5}$

$x = \dfrac{2\cdot 2}{5\cdot 5}$

$x = \dfrac{4}{25}.$

d) $(-0,2) – \dfrac{1}{6}x = \dfrac{2}{3}$

$\dfrac{1}{6}x = -0,2 – \dfrac{2}{3}$

$\dfrac{1}{6}x = \dfrac{-1}{5} – \dfrac{2}{3}$

$\dfrac{1}{6}x = \dfrac{-3}{15} – \dfrac{10}{15}$

$\dfrac{1}{6}x = \dfrac{-13}{15}$

$x = \dfrac{-13}{15} : \dfrac{1}{6}$

$x = \dfrac{-13}{15}\cdot 6$

$x = \dfrac{-13\cdot 2}{5}$

$x = \dfrac{-26}{5}.$

Bài tập 11:

a) $x : \dfrac{1}{2} = \dfrac{-2}{3} – \dfrac{2}{5}$

$x : \dfrac{1}{2} = \dfrac{-10}{15} – \dfrac{6}{15}$

$x:\dfrac{1}{2} = \dfrac{-16}{15}$

$x = \dfrac{-16}{15} \cdot \dfrac{1}{2}$

$x = \dfrac{-8}{15}.$

b) $\dfrac{-4}{5} – x : \dfrac{1}{3} = \dfrac{1}{2}$

$x : \dfrac{1}{3} = \dfrac{-4}{5} – \dfrac{1}{2}$

$x : \dfrac{1}{3} = \dfrac{-8}{10} – \dfrac{5}{10}$

$x : \dfrac{1}{3} = \dfrac{-13}{10}$

$x = \dfrac{-13}{10} \cdot \dfrac{1}{3}$

$x = \dfrac{-13}{30}.$

c) $\dfrac{4}{3} + \dfrac{5}{8} : x = \dfrac{1}{12}$

$\dfrac{5}{8} : x = \dfrac{1}{12} – \dfrac{4}{3}$

$\dfrac{5}{8} : x = \dfrac{1}{12} – \dfrac{16}{12}$

$\dfrac{5}{8} : x = \dfrac{-15}{12}$

$\dfrac{5}{8} : x = \dfrac{-5}{4}$

$x = \dfrac{5}{8} : \dfrac{-5}{4}$

$x = \dfrac{5}{8}\cdot \dfrac{-4}{5}$

$x = \dfrac{-1}{2}.$

d) $\left(-0,75x + \dfrac{5}{2}\right)\cdot \dfrac{4}{7} = \dfrac{-1}{3}$

$-0,75x + \dfrac{5}{2} = \dfrac{-1}{3} : \dfrac{4}{7}$

$-0,75x +\dfrac{5}{2} = \dfrac{-1}{3}\cdot \dfrac{7}{4}$

$-0,75x + \dfrac{5}{2} = \dfrac{-7}{12}$

$-0,75x = \dfrac{-7}{12} – \dfrac{5}{2}$

$-0,75x = \dfrac{-7}{12} – \dfrac{30}{12}$

$-0,75x = \dfrac{-37}{12}$

$x = \dfrac{-37}{12} : (-0,75)$

$x = \dfrac{-37}{9}.$