To classify the equations in the image as having "No Solution," "One Solution," or "Infinitely Many Solutions," I will break each equation down mathematically:

1. Equation: -4x + 4x = 0

   • Simplify: $0 = 0$.
   • This is always true, meaning there are Infinitely Many Solutions.

2. Equation: -x = 7x - 8x

   • Simplify $7x - 8x = -x$: $-x = -x$.
   • After simplifying, it becomes $0 = 0$, so there are Infinitely Many Solutions.

3. Equation: 5 - x = -x

   • Simplify: $5 = 0$, which is a contradiction.
   • Therefore, this equation has No Solution.

4. **Equation: x + = =

Let's analyze each equation step by step based on the uploaded image:

1. Equation: -4x + 4x = 0

   • Simplify: $-4x + 4x = 0 \rightarrow 0 = 0$.
   • This is always true, meaning there are Infinitely Many Solutions.

2. Equation: -x = 7x - 8x

   • Simplify: $-x = 7x - 8x \rightarrow -x = -x$.
   • This is always true for any $x$, meaning there are Infinitely Many Solutions.

3. Equation: 5 - x = -x

   • Simplify: $5 - x = -x \rightarrow 5 = 0$ (contradiction).
   • Since this leads to a false statement, the equation has No Solution.

4. Equation: x + 4 = x + 3

   • Simplify: $x + 4 = x + 3 \rightarrow 4 = 3$ (contradiction).
   • This leads to a false statement, so the equation has No Solution.

5. Equation: 6x - (3x + 8) = 16

   • Simplify: $6x - 3x - 8 = 16 \rightarrow 3x - 8 = 16 \rightarrow 3x = 24 \rightarrow x = 8$.
   • This gives a specific solution ($x = 8$), so it has One Solution.

6. Equation: 9 = 3(5x - 2)

   • Simplify: $9 = 15x - 6 \rightarrow 15x = 15 \rightarrow x = 1$.
   • This gives a specific solution ($x = 1$), so it has One Solution.

Classification:

• No Solution: $x + 4 = x + 3$, $5 - x = -x$.
• One Solution: $6x - (3x + 8) = 16$, $9 = 3(5x - 2)$.
• Infinitely Many Solutions: $-4x + 4x = 0$, $-x = 7x - 8x$.

Would you like a further breakdown or explanation of any specific equation?

Related Questions:

1. How can you identify if an equation has infinitely many solutions?
2. What types of equations result in "no solution" scenarios?
3. Can you provide examples of equations with exactly one solution?
4. What are the key steps to simplify equations like these?
5. How can you verify your solution after solving the equation?

Tip: Always simplify equations fully to check for contradictions or tautologies, which help determine the type of solution.