19. higher order thinking write one equation that has one solution, one equation that has no solution, and…

Explanation:

One - solution equation

Step1: Consider a linear equation

For a linear equation (ax + b=0) ((a\neq0)), it has one solution. Let (a = 2) and (b=-4). The equation (2x-4 = 0).

Step2: Solve the equation

Add (4) to both sides: (2x=4). Divide both sides by (2): (x = 2).

No - solution equation

Step1: Create a contradiction

Start with (3x+5=3x + 7).

Step2: Subtract (3x) from both sides

(3x - 3x+5=3x - 3x+7), which simplifies to (5 = 7) (a contradiction, so no solution).

Infinitely - many - solutions equation

Step1: Create an identity

Take (4x+6=2(2x + 3)).

Step2: Expand the right - hand side

Using the distributive property (a(b + c)=ab+ac) ((a = 2), (b = 2x), (c = 3)), we get (4x+6=4x+6). Subtract (4x) from both sides: (6=6). This is an identity, and any value of (x) will satisfy the equation.

Answer:

• One - solution equation: (2x-4 = 0)
• No - solution equation: (3x + 5=3x+7)
• Infinitely - many - solutions equation: (4x + 6=2(2x + 3))