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Solve the inequality 7(3x-3) < -6(c+8).

Options:
A) x < -2c - 13
B) x > -2c - 13
C) x < -2c + 13
D) x > -2c + 13

User Tambler
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1 Answer

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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.

User Tomasz Iniewicz
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