b. \( \frac{3}{4} x+\frac{2}{3}=\frac{3}{8}+\frac{5}{6} \) c. \( \frac{1}{5} x+\frac{2}{3}=\frac{3}{8}+\frac{3}{5} \) d. \( \frac{2}{3}(x-1)+2=\frac{2}{3}+\frac{12}{10} \cdot \frac{5}{3} \) e. \( \frac{5}{10} x+7=\frac{4}{3}-\left(x-\frac{7}{3}\right) \) f \( \cdot \frac{3}{4} x-\frac{7}{9}=\frac{2}{7} \cdot\left(\frac{3}{2} x+\frac{14}{3}\right) \)

Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{3}{4}x+\frac{2}{3}=\frac{3}{8}+\frac{5}{6}\) - step1: Add the numbers: \(\frac{3}{4}x+\frac{2}{3}=\frac{29}{24}\) - step2: Move the constant to the right side: \(\frac{3}{4}x=\frac{29}{24}-\frac{2}{3}\) - step3: Subtract the numbers: \(\frac{3}{4}x=\frac{13}{24}\) - step4: Multiply by the reciprocal: \(\frac{3}{4}x\times \frac{4}{3}=\frac{13}{24}\times \frac{4}{3}\) - step5: Multiply: \(x=\frac{13}{18}\) Solve the equation \( \frac{1}{5} x+\frac{2}{3}=\frac{3}{8}+\frac{3}{5} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{1}{5}x+\frac{2}{3}=\frac{3}{8}+\frac{3}{5}\) - step1: Add the numbers: \(\frac{1}{5}x+\frac{2}{3}=\frac{39}{40}\) - step2: Move the constant to the right side: \(\frac{1}{5}x=\frac{39}{40}-\frac{2}{3}\) - step3: Subtract the numbers: \(\frac{1}{5}x=\frac{37}{120}\) - step4: Multiply by the reciprocal: \(\frac{1}{5}x\times 5=\frac{37}{120}\times 5\) - step5: Multiply: \(x=\frac{37}{24}\) Solve the equation \( \frac{3}{4} x-\frac{7}{9}=\frac{2}{7} \cdot\left(\frac{3}{2} x+\frac{14}{3}\right) \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{3}{4}x-\frac{7}{9}=\frac{2}{7}\left(\frac{3}{2}x+\frac{14}{3}\right)\) - step1: Multiply the terms: \(\frac{3}{4}x-\frac{7}{9}=\frac{3}{7}x+\frac{4}{3}\) - step2: Multiply both sides of the equation by LCM: \(\left(\frac{3}{4}x-\frac{7}{9}\right)\times 252=\left(\frac{3}{7}x+\frac{4}{3}\right)\times 252\) - step3: Calculate: \(189x-196=\left(\frac{3}{7}x+\frac{4}{3}\right)\times 252\) - step4: Calculate: \(189x-196=108x+336\) - step5: Move the expression to the left side: \(189x-108x=336+196\) - step6: Add and subtract: \(81x=336+196\) - step7: Add and subtract: \(81x=532\) - step8: Divide both sides: \(\frac{81x}{81}=\frac{532}{81}\) - step9: Divide the numbers: \(x=\frac{532}{81}\) Solve the equation \( \frac{2}{3}(x-1)+2=\frac{2}{3}+\frac{12}{10} \cdot \frac{5}{3} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{2}{3}\left(x-1\right)+2=\frac{2}{3}+\frac{12}{10}\times \frac{5}{3}\) - step1: Simplify: \(\frac{2}{3}x+\frac{4}{3}=\frac{8}{3}\) - step2: Move the constant to the right side: \(\frac{2}{3}x=\frac{8}{3}-\frac{4}{3}\) - step3: Subtract the numbers: \(\frac{2}{3}x=\frac{4}{3}\) - step4: Multiply by the reciprocal: \(\frac{2}{3}x\times \frac{3}{2}=\frac{4}{3}\times \frac{3}{2}\) - step5: Multiply: \(x=2\) Solve the equation \( \frac{5}{10} x+7=\frac{4}{3}-\left(x-\frac{7}{3}\right) \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{5}{10}x+7=\frac{4}{3}-\left(x-\frac{7}{3}\right)\) - step1: Reduce the fraction: \(\frac{1}{2}x+7=\frac{11}{3}-x\) - step2: Multiply both sides of the equation by LCM: \(\left(\frac{1}{2}x+7\right)\times 6=\left(\frac{11}{3}-x\right)\times 6\) - step3: Calculate: \(3x+42=\left(\frac{11}{3}-x\right)\times 6\) - step4: Calculate: \(3x+42=22-6x\) - step5: Move the expression to the left side: \(3x+6x=22-42\) - step6: Add and subtract: \(9x=22-42\) - step7: Add and subtract: \(9x=-20\) - step8: Divide both sides: \(\frac{9x}{9}=\frac{-20}{9}\) - step9: Divide the numbers: \(x=-\frac{20}{9}\) Aquí están las soluciones para cada una de las ecuaciones: b. Para la ecuación \( \frac{3}{4} x+\frac{2}{3}=\frac{3}{8}+\frac{5}{6} \): - La solución es \( x=\frac{13}{18} \) o \( x=0.7\dot{2} \). c. Para la ecuación \( \frac{1}{5} x+\frac{2}{3}=\frac{3}{8}+\frac{3}{5} \): - La solución es \( x=\frac{37}{24} \) o \( x=1.541\dot{6} \). d. Para la ecuación \( \frac{2}{3}(x-1)+2=\frac{2}{3}+\frac{12}{10} \cdot \frac{5}{3} \): - La solución es \( x=2 \). e. Para la ecuación \( \frac{5}{10} x+7=\frac{4}{3}-\left(x-\frac{7}{3}\right) \): - La solución es \( x=-\frac{20}{9} \) o \( x=-2.\dot{2} \). f. Para la ecuación \( \frac{3}{4} x-\frac{7}{9}=\frac{2}{7} \cdot\left(\frac{3}{2} x+\frac{14}{3}\right) \): - La solución es \( x=\frac{532}{81} \). Si necesitas más detalles sobre cómo se resolvieron estas ecuaciones, házmelo saber.