1. create a single variable linear equation that has no solution. solve the equation algebraically to prove that it does not have a solution. 2. create a single variable linear equation that has one solution. solve the equation algebraically to prove that there is one distinct solution for the equation. 3. create a single variable linear equation that has infinitely many solutions. solve the equation algebraically to prove that there is an infinite number of solutions for the equation

1. a single variable linear equation that has no solution

x + 4 = x + 5

x - x = 5 - 4

0 = 1 (which is false)

2. a single variable linear equation that has one solution

2x + 4 = x + 5

2x  - x = 5 - 4

x = 1

3. a single variable linear equation that has infinitely many solutions

x + 4 - 1= x + 3 

x - x = 3 - 4 + 1

0 = 0 (identity)

what's that

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i