Final answer:
The equations 2x - 3 = 5 and 4x = 16 both have the same solution, x = 4. This is determined by using addition, subtraction, multiplication, and division to isolate x in each equation.
Step-by-step explanation:
We can solve the equation 2x - 3 = 5 by adding 3 to both sides, following the principle that addition or subtraction of the same number on the two sides of an equation does not change the equality. This gives us 2x = 8. Dividing both sides by 2, we get x = 4, which is the solution to the first equation.
Similarly, for the equation 4x = 16, we can divide both sides by 4, which, as per the rules of mathematics, does not change the equality. This gives us the same solution: x = 4.
Since both equations yield the same solution, x = 4, we can say that the two equations 2x - 3 = 5 and 4x = 16 indeed have the same solution.