Solve the following inequality for cc. Write your answer in simplest form.
minus, 7, c, minus, left bracket, 2, c, plus, 2, right bracket, is greater than, minus, 4, c, minus, 2, plus, 6, c
−7c−(2c+2)>
−4c−2+6c
-7c - (2c + 2) > -4c - 2 + 6c
Distribute the negative sign: -7c - 2c - 2 > -4c - 2 + 6c
Combine like terms on both sides: -9c - 2 > 2c - 2
Add 9c to both sides: -2 > 2c - 2 + 9c
Combine like terms: -2 > 11c - 2
Add 2 to both sides: 0 > 11c
Divide by 11: 0/11 > c
Simplify: 0 > c
The solution is: c < 0
To solve the inequality, let's simplify both sides step by step:
First, distribute the negative sign to the expression inside the parentheses on the left side:
-7c - 2c - 2 > -4c - 2 + 6c
Next, combine like terms on each side:
-9c - 2 > 2c - 2
Then, add 9c to both sides to isolate the variable:
-9c + 9c - 2 > 2c - 2 + 9c
-2 > 11c - 2
Now, add 2 to both sides to isolate the term with the variable:
-2 + 2 > 11c - 2 + 2
0 > 11c
Finally, divide both sides by 11 (remembering to flip the inequality sign since we are dividing by a negative number):
0/11 < 11c/11
0 < c
Therefore, the solution to the inequality is c > 0.
To solve this inequality for cc, we need to simplify both sides of the equation and then isolate cc on one side.
Let's simplify the left side:
-7c - (2c + 2)
First, let's simplify the expression inside the parentheses.
-7c - 2c - 2
Combining like terms, we get:
-9c - 2
Now let's simplify the right side:
-4c - 2 + 6c
Combining like terms, we get:
2c - 2
Now we have:
-9c - 2 > 2c - 2
Next, let's isolate cc on one side by moving all terms involving cc to one side and the constant terms to the other side:
-9c - 2 - 2c + 2 > 2c - 2 - 2c
Combine like terms:
-11c > -4
Divide by -11 to solve for cc and remember that whenever you divide an inequality by a negative number, the direction of the inequality sign switches:
c < 4/11
So the solution to the inequality is cc is less than 4/11.