Question

solve the linear equation for c.
if no solution exists, enter no solution. if the equation has infinite solutions, enter all real numbers.
\\(-3 \left(-2c - 2\
ight) + 54 = 2 \left(-c - 2\
ight)\\)
show your work here

Explanation:

Step1: Distribute the terms

First, we distribute the -3 on the left side and the 2 on the right side of the equation:
\(-3(-2c - 2) = 6c + 6\) and \(2(-c - 2) = -2c - 4\)
So the equation becomes:
\(6c + 6 + 54 = -2c - 4\)

Step2: Combine like terms

On the left side, we combine the constant terms:
\(6c + 60 = -2c - 4\)

Step3: Add 2c to both sides

We add \(2c\) to both sides to get all the \(c\) terms on one side:
\(6c + 2c + 60 = -4\)
\(8c + 60 = -4\)

Step4: Subtract 60 from both sides

We subtract 60 from both sides to isolate the term with \(c\):
\(8c = -4 - 60\)
\(8c = -64\)

Step5: Divide by 8

We divide both sides by 8 to solve for \(c\):
\(c = \frac{-64}{8}\)
\(c = -8\)

Answer:

\(c = -8\)