Question

Determine the solution type for the equation 8 + c = 5c - 4(c + 5).

A) One solution, c = -8
B) No solution
C) Infinite solutions
D) One solution, c = 4

Answer 1

After simplifying the given equation, we find that it simplifies to a false statement (8 = -20), indicating that there is no solution to the equation.

Step-by-step explanation:

To determine the solution type for the equation 8 + c = 5c - 4(c + 5), we first simplify the equation.

1. Expand the right side of the equation: 5c - 4(c + 5) becomes 5c - 4c - 20.
2. Simplify the right side by combining like terms: 5c - 4c - 20 simplifies to c - 20.
3. Now we have the simplified equation: 8 + c = c - 20.
4. Subtract c from both sides to get all the c terms on one side: 8 = -20.
5. The variable c cancels out, and we are left with a false statement, 8 = -20, which indicates that there is no solution.

The solution type for the equation 8 + c = 5c - 4(c + 5) is (B) No solution.