Final answer:
The equation has an infinite number of solutions because upon simplification both sides of the equation yield an identity (0 = 0), indicating the equation is true for any value of x.
Step-by-step explanation:
The equation 7x + 13x - 5 - 15 = -10 - 10 + 14x + 6x has an infinite amount of solutions because when simplified, it becomes an identity. To see why this is the case, let's combine like terms on each side:
- On the left-hand side, we have 7x + 13x, which simplifies to 20x. The constants -5 and -15 combine to -20.
- On the right-hand side, -10 - 10 simplifies to -20, and 14x + 6x simplifies to 20x.
After simplifying both sides, we have 20x - 20 = 20x - 20, which simplifies further to 0 = 0. This shows us that the equation is true for any value of x, hence an infinite number of solutions.