Question

a.   3(x-1/2) - 5(x+3/5=-x+1/5

b.   2/3× + 1/2x = 5/2:15/4

c.   3x + 2x = 5/8 × 4/3 

d.   17/2 - |2x - 3/4| = -7/4

e.   (x + 1/25) + 17/25 = 26/25

f.    2/3x - 1/2x = 5/12

g.   (x + 1/2) × (2/3-2x) = 0

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Answer 1

g. \(\left(x+\frac{1}{2}\right)\left(\frac{2}{3}-2x\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{2}=0\\\frac{2}{3}-2x=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{-1}{2}\\x=\frac{1}{3}\end{cases}}\)

Vậy \(x\in\left\{\frac{-1}{2};\frac{1}{3}\right\}\)

Answer 2

f. \(\frac{2}{3}x-\frac{1}{2}x=\frac{5}{12}\)

\(\Leftrightarrow x\left(\frac{2}{3}-\frac{1}{2}\right)=\frac{5}{12}\)

\(\Leftrightarrow x\left(\frac{4}{6}-\frac{3}{6}\right)=\frac{5}{12}\)

\(\Leftrightarrow\frac{1}{6}x=\frac{5}{12}\)

\(\Leftrightarrow x=\frac{5}{12}\div\frac{1}{6}\)

\(\Leftrightarrow x=\frac{30}{12}=\frac{5}{2}\)

Answer 3

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

\(\Leftrightarrow x\left(3+2\right)=\frac{5.4}{8.3}\)

\(\Leftrightarrow5x=\frac{5.1}{2.3}\)

\(\Leftrightarrow5x=\frac{5}{6}\)

\(\Leftrightarrow x=\frac{5}{6}\div5\)

\(\Leftrightarrow x=\frac{1}{6}\)

Answer 4

\(\frac{2}{3}x+\frac{1}{2}x=\frac{5}{2}\div\frac{15}{4}\)

\(\Leftrightarrow x\left(\frac{2}{3}+\frac{1}{2}\right)=\frac{5}{2}\times\frac{15}{4}\)

\(\Leftrightarrow x\left(\frac{4}{6}+\frac{3}{6}\right)=\frac{75}{8}\)

\(\Leftrightarrow\frac{7}{6}x=\frac{75}{8}\)

\(\Leftrightarrow x=\frac{75}{8}\div\frac{7}{6}\)

\(\Leftrightarrow x=\frac{75}{8}\times\frac{6}{7}\)

\(\Leftrightarrow x=\frac{225}{28}\)

Answer 5

\(\left(x+\frac{1}{25}\right)+\frac{17}{25}=\frac{26}{25}\)

\(\Leftrightarrow x+\frac{1}{25}=\frac{26}{25}-\frac{17}{25}\)

\(\Leftrightarrow x+\frac{1}{25}=\frac{9}{25}\)

\(\Leftrightarrow x=\frac{9}{25}-\frac{1}{25}\)

\(\Leftrightarrow x=\frac{8}{25}\)

Answer 6

d. \(\frac{17}{2}-\left|2x-\frac{3}{4}\right|=\frac{-7}{4}\)

\(\Leftrightarrow\left|2x-\frac{3}{4}\right|=\frac{17}{2}+\frac{7}{4}\)

\(\Leftrightarrow\left|2x-\frac{3}{4}\right|=\frac{34}{4}+\frac{7}{4}\)

\(\Leftrightarrow\left|2x-\frac{3}{4}\right|=\frac{41}{4}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-\frac{3}{4}=\frac{41}{4}\\2x-\frac{3}{4}=\frac{-41}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=5,5\\x=\frac{-19}{4}\end{cases}}\)

Answer 7

a. \(3\left(x-\frac{1}{2}\right)-5\left(x+\frac{3}{5}\right)=-x+\frac{1}{5}\)

\(\Leftrightarrow3x-\frac{3}{2}-5x-3=\frac{1}{5}-x\)

\(\Leftrightarrow\left(3x-5x\right)-\left(\frac{3}{2}+3\right)=\frac{1}{5}-x\)

\(\Leftrightarrow-2x-\left(\frac{3}{2}+\frac{6}{2}\right)=\frac{1}{5}-x\)

\(\Leftrightarrow-2x-\frac{9}{2}=\frac{1}{5}-x\)

\(\Leftrightarrow-2x+x=\frac{1}{5}+\frac{9}{2}\)

\(\Leftrightarrow-x=\frac{2}{10}+\frac{45}{10}\)

\(\Leftrightarrow-x=\frac{47}{10}\)

\(\Leftrightarrow x=\frac{-47}{10}\)