Final answer:
An example of an equation with variables on both sides that is an identity is 2x + 3 = 3x + 4, which simplifies to 1 = 1. An example of an equation with variables on both sides that has no solution is 2x + 1 = 2x + 5, which leads to an inconsistent statement 1 = 5.
Step-by-step explanation:
To give an example of an equation with variables on both sides that is an identity, let's take the equation 2x + 3 = 3x + 4. To solve this equation, we can subtract 2x from both sides, which gives us 3 = x + 4. Then, subtracting 4 from both sides, we find that -1 = x. So, the solution to the equation is x = -1. When we substitute x = -1 back into the original equation, we get 2(-1) + 3 = 3(-1) + 4, which simplifies to 1 = 1. Since this equation holds true for any value of x, it is an identity.
For an example of an equation with variables on both sides that has no solution, let's consider the equation 2x + 1 = 2x + 5. If we subtract 2x from both sides, we get 1 = 5. However, this is not possible since 1 cannot equal 5. Therefore, the equation has no solution.