Question

Question:

Out of these six problems which two are infinite solutions and which two have no solution and which two have one solution

1. 2x + 3 = 2x + 7
2. 7x + 3 = 7x + 3
3. 4x + 22 = 8x + 10
4. 5x + 5 = 5x + 4
5. 3x + 18 = 5x + 8
6. 3(4x + 8) = 4(3x + 6)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The problems that have infinite solutions are:

2. 7x + 3 = 7x + 3 (same equation on both sides)
5. 3x + 18 = 5x + 8 (equation simplifies to 0 = 0)

The problems that have no solution are:

1. 2x + 3 = 2x + 7 (equation simplifies to 3 = 7, which is not true)
4. 5x + 5 = 5x + 4 (equation simplifies to 5 = 4, which is not true)

The problems that have one solution are:

3. 4x + 22 = 8x + 10 (solving gives x = 3)
6. 3(4x + 8) = 4(3x + 6) (solving gives x = -6)

Answer 2

What do you notice about equations that are in each of these categories?

Answer 3

[AI-generated answer — Bot GPT 3.5]

Looking at the equations in each category:

Infinite Solutions:
- The equations in this category involve expressions that are equal on both sides. This means that the variables can be any value and the equation will still hold true.

No Solution:
- The equations in this category involve contradictory statements, such as 3 = 7 or 5 = 4. These statements are never true, so the equations have no solutions.

One Solution:
- The equations in this category have distinct values for the variable that make the equation true. This usually involves simplifying the equation to a point where there is a clear solution.

Answer 4

Can you make that into steps or bullet points or a paragraph?

Answer 5

[AI-generated answer — Bot GPT 3.5]

Sure, here is the information broken down into bullet points:

- Equations with infinite solutions have expressions that are equal on both sides, allowing for any value of the variable to hold true.
- Equations with no solution involve contradictory statements that can never be true, such as 3 = 7 or 5 = 4.
- Equations with one solution have distinct values for the variable that make the equation true, usually reached by simplifying the equation to a point where there is a clear solution.