Final answer:
To solve the equation, distribute the fractions, combine like terms, and isolate b. After simplifying, the solution is found to be b = -3. Checking the solution in the original equation confirms its correctness.
Step-by-step explanation:
To solve the equation 4/5(-1 + 3b) = 2/5(5b + 10) - 2, we will first distribute the fractions on both sides of the equation. This gives us:
-4/5 + 12/5b = 2b + 4 - 2.
Next, we'll combine like terms and simplify the equation:
- 12/5b - 2b = 4/5 - 2,
- (12/5 - 10/5)b = 4/5 - 10/5,
- 2/5b = -6/5.
To isolate b, we multiply both sides by 5/2. This gives us b = -3. To check the solution, we substitute b back into the original equation.
If b = -3, then 4/5(-1 + 3(-3)) = 2/5(5(-3) + 10) - 2, which simplifies to -4/5 - 36/5 = -30/5 + 4 - 2. This further simplifies to -40/5 = -40/5, confirming that the solution b = -3 is correct.