14. Solve each equation algebraically. a. \( 7 a=63 \) b. \( 2 \cdot 3 b=36.8 \) c. \( 12=1.5 x \) d. \( \frac{3}{5} x=21 \) e. \( \frac{3}{5} x=\frac{12}{25} \) f. \( \frac{5}{7} n=\frac{15}{28} \)

Here are the solutions: a. 7a = 63   Divide both sides by 7:    a = 63 ÷ 7 = 9 b. 2 · 3b = 36.8   Interpret 2 · 3b as (2)(3b) = 6b. Then:    6b = 36.8   Divide both sides by 6:    b = 36.8 ÷ 6    b = 6.1333… (which can also be expressed as 92/15 if an exact fraction is desired) c. 12 = 1.5x   Divide both sides by 1.5:    x = 12 ÷ 1.5 = 8 d. (3/5)x = 21   Multiply both sides by the reciprocal of 3/5, which is 5/3:    x = 21 × (5/3) = 105/3 = 35 e. (3/5)x = (12/25)   Multiply both sides by the reciprocal of 3/5 (i.e., 5/3):    x = (12/25) × (5/3) = (12×5)/(25×3) = 60/75   Simplify by dividing numerator and denominator by 15:    x = (60÷15)/(75÷15) = 4/5 f. (5/7)n = (15/28)   Multiply both sides by the reciprocal of 5/7, which is 7/5:    n = (15/28) × (7/5) = (15×7)/(28×5) = 105/140   Simplify by dividing numerator and denominator by 35:    n = (105÷35)/(140÷35) = 3/4 These are your solutions.