Question

Determine the solution type for each equation. If one solution, determine the value for (x).

2(e + 10) = 8 - (-2e - 12)

A) One solution: (x = -2)
B) One solution: (x = 8)
C) No solution
D) Infinite solutions

Answer 1

Upon simplifying the equation, 2(e + 10) = 8 - (-2e - 12), we find that the variable terms cancel out and we are left with a true statement, indicating that there are infinite solutions to this equation.

Step-by-step explanation:

To determine the solution type for each equation, we start by simplifying and solving:

2(e + 10) = 8 - (-2e - 12)

First, distribute the 2 on the left side of the equation:

2e + 20 = 8 - (-2e - 12)

Next, simplify the right side by removing the parentheses and changing the signs inside:

2e + 20 = 8 + 2e + 12

Combining like terms on the right gives us:

2e + 20 = 2e + 20

Now, we can see that the e terms on both sides of the equation are the same. So, when we try to isolate e, we get a tautology (something that's always true):

20 = 20

Since the variables have cancelled out and we are left with a true statement, this means that the equation has infinite solutions. Therefore, the correct answer is:

D) Infinite solutions