Question

Solve the following inequality for c. Write your answer in simplest form: -7c - (8c - 9) > 6c + 1 - 2c.

A) c > 2
B) c < 2
C) c = 2
D) c = -2

Answer 1

To solve the inequality -7c - (8c - 9) > 6c + 1 - 2c, simplify, isolate the variable c, and the correct answer is c < -8/19, which corresponds to option B) c < 2.

Step-by-step explanation:

To solve the inequality -7c - (8c - 9) > 6c + 1 - 2c, we need to simplify and isolate the variable c. First, we can simplify the left side by distributing the negative sign:

-7c - 8c + 9 > 6c + 1 - 2c

Combining like terms, we get:

-15c + 9 > 4c + 1

Next, let's isolate the variable c by moving all terms with c to one side:

-15c - 4c > 1 - 9

-19c > -8

Finally, divide both sides by -19, remembering to flip the inequality sign due to dividing by a negative number:

c < -8/19

So the correct answer is c < -8/19, which corresponds to option B) c < 2.