a. $$ \frac{4}{5} x+\frac{2}{3}=\frac{3}{5}+\frac{2}{15} \cdot 2 $$ b. $$ \frac{3}{4} x+\frac{2}{3}=\frac{3}{8}+\frac{5}{5} $$ c. $$ \frac{1}{5} x+\frac{7}{3}=\frac{3}{8}+\frac{3}{5} $$ d. $$ \frac{2}{3}(x-7)+2=\frac{2}{3}+\frac{72}{10} \cdot \frac{5}{3} $$ e. $$ \frac{5}{10} x+7=\frac{4}{3}-\left(x-\frac{7}{3}\right) $$ f. $$ \frac{3}{4} x-\frac{7}{9}=\frac{2}{7} \cdot\left(\frac{3}{2} x+\frac{24}{3}\right) $$

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UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{1}{5}x+\frac{7}{3}=\frac{3}{8}+\frac{3}{5}$$
- step1: Add the numbers:
  $$\frac{1}{5}x+\frac{7}{3}=\frac{39}{40}$$
- step2: Move the constant to the right side:
  $$\frac{1}{5}x=\frac{39}{40}-\frac{7}{3}$$
- step3: Subtract the numbers:
  $$\frac{1}{5}x=-\frac{163}{120}$$
- step4: Multiply by the reciprocal:
  $$\frac{1}{5}x	imes 5=-\frac{163}{120}	imes 5$$
- step5: Multiply:
  $$x=-\frac{163}{24}$$
Solve the equation $$ \frac{3}{4} x-\frac{7}{9}=\frac{2}{7} \cdot\left(\frac{3}{2} x+\frac{24}{3}ight) $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{3}{4}x-\frac{7}{9}=\frac{2}{7}\left(\frac{3}{2}x+\frac{24}{3}ight)$$
- step1: Simplify:
  $$\frac{3}{4}x-\frac{7}{9}=\frac{3}{7}x+\frac{16}{7}$$
- step2: Multiply both sides of the equation by LCM:
  $$\left(\frac{3}{4}x-\frac{7}{9}ight)	imes 252=\left(\frac{3}{7}x+\frac{16}{7}ight)	imes 252$$
- step3: Calculate:
  $$189x-196=\left(\frac{3}{7}x+\frac{16}{7}ight)	imes 252$$
- step4: Calculate:
  $$189x-196=108x+576$$
- step5: Move the expression to the left side:
  $$189x-108x=576+196$$
- step6: Add and subtract:
  $$81x=576+196$$
- step7: Add and subtract:
  $$81x=772$$
- step8: Divide both sides:
  $$\frac{81x}{81}=\frac{772}{81}$$
- step9: Divide the numbers:
  $$x=\frac{772}{81}$$
Solve the equation $$ \frac{2}{3}(x-7)+2=\frac{2}{3}+\frac{72}{10} \cdot \frac{5}{3} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{2}{3}\left(x-7ight)+2=\frac{2}{3}+\frac{72}{10}	imes \frac{5}{3}$$
- step1: Simplify:
  $$\frac{2}{3}x-\frac{8}{3}=\frac{38}{3}$$
- step2: Move the constant to the right side:
  $$\frac{2}{3}x=\frac{38}{3}+\frac{8}{3}$$
- step3: Add the numbers:
  $$\frac{2}{3}x=\frac{46}{3}$$
- step4: Multiply by the reciprocal:
  $$\frac{2}{3}x	imes \frac{3}{2}=\frac{46}{3}	imes \frac{3}{2}$$
- step5: Multiply:
  $$x=23$$
Solve the equation $$ \frac{3}{4} x+\frac{2}{3}=\frac{3}{8}+\frac{5}{5} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{3}{4}x+\frac{2}{3}=\frac{3}{8}+\frac{5}{5}$$
- step1: Simplify:
  $$\frac{3}{4}x+\frac{2}{3}=\frac{11}{8}$$
- step2: Move the constant to the right side:
  $$\frac{3}{4}x=\frac{11}{8}-\frac{2}{3}$$
- step3: Subtract the numbers:
  $$\frac{3}{4}x=\frac{17}{24}$$
- step4: Multiply by the reciprocal:
  $$\frac{3}{4}x	imes \frac{4}{3}=\frac{17}{24}	imes \frac{4}{3}$$
- step5: Multiply:
  $$x=\frac{17}{18}$$
Solve the equation $$ \frac{4}{5} x+\frac{2}{3}=\frac{3}{5}+\frac{2}{15} \cdot 2 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{4}{5}x+\frac{2}{3}=\frac{3}{5}+\frac{2}{15}	imes 2$$
- step1: Simplify:
  $$\frac{4}{5}x+\frac{2}{3}=\frac{13}{15}$$
- step2: Move the constant to the right side:
  $$\frac{4}{5}x=\frac{13}{15}-\frac{2}{3}$$
- step3: Subtract the numbers:
  $$\frac{4}{5}x=\frac{1}{5}$$
- step4: Multiply by the reciprocal:
  $$\frac{4}{5}x	imes \frac{5}{4}=\frac{1}{5}	imes \frac{5}{4}$$
- step5: Multiply:
  $$x=\frac{1}{4}$$
Solve the equation $$ \frac{5}{10} x+7=\frac{4}{3}-\left(x-\frac{7}{3}ight) $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{5}{10}x+7=\frac{4}{3}-\left(x-\frac{7}{3}ight)$$
- step1: Reduce the fraction:
  $$\frac{1}{2}x+7=\frac{11}{3}-x$$
- step2: Multiply both sides of the equation by LCM:
  $$\left(\frac{1}{2}x+7ight)	imes 6=\left(\frac{11}{3}-xight)	imes 6$$
- step3: Calculate:
  $$3x+42=\left(\frac{11}{3}-xight)	imes 6$$
- 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:

a. Para la ecuación $$ \frac{4}{5} x+\frac{2}{3}=\frac{3}{5}+\frac{2}{15} \cdot 2 $$:
   - La solución es $$ x = \frac{1}{4} $$ o $$ x = 0.25 $$.

b. Para la ecuación $$ \frac{3}{4} x+\frac{2}{3}=\frac{3}{8}+\frac{5}{5} $$:
   - La solución es $$ x = \frac{17}{18} $$ o $$ x = 0.9\dot{4} $$.

c. Para la ecuación $$ \frac{1}{5} x+\frac{7}{3}=\frac{3}{8}+\frac{3}{5} $$:
   - La solución es $$ x = -\frac{163}{24} $$ o $$ x = -6.791\dot{6} $$.

d. Para la ecuación $$ \frac{2}{3}(x-7)+2=\frac{2}{3}+\frac{72}{10} \cdot \frac{5}{3} $$:
   - La solución es $$ x = 23 $$.

e. Para la ecuación $$ \frac{5}{10} x+7=\frac{4}{3}-\left(x-\frac{7}{3}ight) $$:
   - La solución es $$ x = -\frac{20}{9} $$ o $$ x = -2.\dot{2} $$.

f. Para la ecuación $$ \frac{3}{4} x-\frac{7}{9}=\frac{2}{7} \cdot\left(\frac{3}{2} x+\frac{24}{3}ight) $$:
   - La solución es $$ x = \frac{772}{81} $$.

Si necesitas más detalles sobre cómo se resolvieron estas ecuaciones, házmelo saber.
a. $$ x = 0.25 $$ b. $$ x = 0.9\dot{4} $$ c. $$ x = -6.791\dot{6} $$ d. $$ x = 23 $$ e. $$ x = -2.\dot{2} $$ f. $$ x = \frac{772}{81} $$

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