Answer:
the number of solutions to the equation 5(2x + 6) = -4(-5 - 2x) is zero.
Explanation:
We can solve the equation 5(2x + 6) = -4(-5 - 2x) by expanding both sides:
5(2x + 6) = -4(-5 - 2x)
10x + 30 = 20 + 8x
2x + 30 = 20
2x = -10
x = -5
However, when we substitute x = -5 back into the original equation, we get:
5(2(-5) + 6) = -4(-5 - 2(-5))
5(-10 + 6) = -4(5 + 10)
5(-4) = -4(15)
-20 = -60
This is a false statement, so there are no solutions to the equation 5(2x + 6) = -4(-5 - 2x).
Another way to see this is to simplify the equation:
5(2x + 6) = -4(-5 - 2x)
10x + 30 = 20 + 8x
2x + 30 = 20
2x = -10
x = -5
At this point, we can substitute x = -5 into either side of the equation and get a false statement, so we know that there are no solutions.
Therefore, the number of solutions to the equation 5(2x + 6) = -4(-5 - 2x) is zero.