Final answer:
The correct answer is option c) x<9. After expanding, combining like terms, and isolating the variable x, the inequality −2(x−3)−11<7x+40 simplifies to x<9, which means the correct answer is option c) x<9.
Step-by-step explanation:
To solve the inequality −2(x−3)−11<7x+40, start by expanding the left side of the inequality:
-2x + 6 - 11 < 7x + 40
Combine like terms to simplify:
-2x - 5 < 7x + 40
Next, add 2x to both sides and subtract 40 from both sides to isolate x:
-5 < 9x + 40 - 40
-5 < 9x
Finally, divide both sides by 9:
−⅓ < x
Since dividing by a positive number doesn't change the direction of the inequality, the final answer is x < 9.