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) $\left(-0,75x + \dfrac{5}{2}\right)\cdot \dfrac{4}{7} = \dfrac{-1}{3}$
$-0,75x + \dfrac{5}{2} = \dfrac{-1}{3} : \dfrac{4}{7}$
$-0,75x +\dfrac{5}{2} = \dfrac{-1}{3}\cdot \dfrac{7}{4}$
$-0,75x + \dfrac{5}{2} = \dfrac{-7}{12}$
$-0,75x = \dfrac{-7}{12} – \dfrac{5}{2}$
$-0,75x = \dfrac{-7}{12} – \dfrac{30}{12}$
$-0,75x = \dfrac{-37}{12}$
$x = \dfrac{-37}{12} : (-0,75)$
$x = \dfrac{-37}{9}.$