Question

write an equation for each number of solutions.
no solution:
one solution:
infinitely many solutions:

Explanation:

Step1: Create no-solution equation

For a linear equation to have no solution, the variable terms must be equal, but the constant terms must be unequal.
Let the equation be $2x + 3 = 2x + 5$

Step2: Create one-solution equation

For a linear equation to have one solution, the variable coefficients must be different.
Let the equation be $2x + 3 = 5x + 9$

Step3: Create infinite-solutions equation

For a linear equation to have infinitely many solutions, both the variable terms and constant terms must be equal (one side is a multiple of the other).
Let the equation be $2(x + 3) = 2x + 6$

Answer:

No solution: $2x + 3 = 2x + 5$
One solution: $2x + 3 = 5x + 9$
Infinitely many solutions: $2(x + 3) = 2x + 6$