b. \( \frac{3}{4} x+\frac{2}{3}=\frac{3}{8}+\frac{5}{6} \)

To solve the equation \( \frac{3}{4} x+\frac{2}{3}=\frac{3}{8}+\frac{5}{6} \), first, let’s simplify the right side. Start by finding a common denominator (which is 24) for \( \frac{3}{8} \) and \( \frac{5}{6} \): - \( \frac{3}{8} = \frac{9}{24} \) - \( \frac{5}{6} = \frac{20}{24} \) So, \( \frac{3}{8} + \frac{5}{6} = \frac{9}{24} + \frac{20}{24} = \frac{29}{24} \). Now your equation looks like this: \[ \frac{3}{4} x + \frac{2}{3} = \frac{29}{24} \] Next, subtract \( \frac{2}{3} \) from both sides. Convert \( \frac{2}{3} \) to have a denominator of 24, so \( \frac{2}{3} = \frac{16}{24} \): \[ \frac{3}{4} x = \frac{29}{24} - \frac{16}{24} = \frac{13}{24} \] To isolate \( x \), multiply both sides by \( \frac{4}{3} \): \[ x = \frac{13}{24} \cdot \frac{4}{3} = \frac{52}{72} \] Finally, simplify \( \frac{52}{72} \) by dividing both numerator and denominator by 4: \[ x = \frac{13}{18} \] And there you have it! The solution to the equation is \( x = \frac{13}{18} \). For further practice with solving similar equations, consider working through problems that involve fractions and different operations—this strengthens your skills! Understanding fractions is not just math; it’s about developing a mindset that can tackle various real-life scenarios, from sharing a pizza with friends to managing recipes in cooking!