org/bookdb.php?title=cc2\&name \( =7.1 .6 \) \&type=lesson entral rSe 2 PDF fles should be printed before use. Use the Fraction Busters to solve the following problems. Hom (ESP) a. \( \frac{3}{2}+\frac{2 x}{5}=\frac{7}{10} \)

To tackle this equation, the best first step is to eliminate the fractions by finding a common denominator. In this case, the least common multiple of the denominators (2, 5, and 10) is 10. Multiply each term of the equation by 10 to simplify the calculations: \[ 10 \times \frac{3}{2} + 10 \times \frac{2x}{5} = 10 \times \frac{7}{10} \] This gives you \( 15 + 4x = 7 \). Now, isolate \( x \) by moving the constant over: \[ 4x = 7 - 15 \] So, \( 4x = -8 \), leading to \( x = -2 \). Voilà! Another common mistake when working with such equations is forgetting to apply the multiplicative factor to every term within an equation, leading to incorrect simplifications. Always double-check that all parts of the equation are adjusted when you scale up to eliminate fractions. Happy solving!