Final answer:
To solve the inequality 4b + 3 (1-2b) > b-9, simplify the expression and isolate the variable b. The solution is b < 6.
Step-by-step explanation:
To solve the inequality 4b + 3 (1-2b) > b-9, we need to simplify the expression and isolate the variable b. Let's start by distributing the 3 to the terms inside the parentheses: 4b + 3 - 6b > b-9. Next, combine like terms on both sides of the equation: -2b + 3 > -9. Subtract 3 from both sides to get -2b > -12. Finally, divide both sides by -2, remembering to flip the inequality sign when dividing by a negative value: b < 6. Therefore, the solution to the inequality is b < 6.