Final answer:
To solve the inequality 7(3x-3) < -6(c+8), simplify both sides of the inequality, isolate the variable, and express the inequality in terms of x and c. The correct answer is C) x < -2c + 13.
Step-by-step explanation:
To solve the inequality 7(3x-3) < -6(c+8), we can start by simplifying both sides of the inequality.
On the left side, distribute the 7 to the terms inside the parentheses: 21x - 21.
On the right side, distribute the -6 to the terms inside the parentheses: -6c - 48.
Now we have the inequality 21x - 21 < -6c - 48. To solve for x, we can isolate the variable by moving all terms with x to one side and all terms with c to the other side. We can do this by adding 6c to both sides and adding 48 to both sides.
This gives us 21x + 6c < -21 + 48. Simplifying further, we get 21x + 6c < 27.
Now, to express this inequality in terms of x and c, we can divide both sides of the inequality by 21. This gives us x + (6/21)c < 27/21, which simplifies to:
x + (2/7)c < 9/7.
Therefore, the correct answer is option C) x < -2c + 13.