Solve the Equation: b - 3⅘ = -8⅗ with Mixed Numbers

To solve this problem, we'll follow these steps:

• Step 1: Convert mixed numbers to improper fractions
• Step 2: Isolate the variable $b$ by applying algebraic operations
• Step 3: Simplify the result to find the value of $b$

Now, let's work through each step:

Step 1: Convert the mixed numbers to improper fractions.
$3\frac{4}{5} = \frac{15}{5} + \frac{4}{5} = \frac{19}{5}$
$-8\frac{3}{5} = -\left(\frac{40}{5} + \frac{3}{5}\right) = -\frac{43}{5}$

Step 2: Add $\frac{19}{5}$ to both sides of the equation to isolate $b$.

$b - \frac{19}{5} = -\frac{43}{5}$

Add $\frac{19}{5}$ to both sides:
$b - \frac{19}{5} + \frac{19}{5} = -\frac{43}{5} + \frac{19}{5}$
This simplifies to:
$b = \frac{-43+19}{5} = \frac{-24}{5} = -4\frac{4}{5}$

Therefore, the solution to the problem is $b = -4\frac{4}{5}$.