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Explanation below

Step-by-step explanation:

First Degree Equations

A first-degree equation can have one, none, or infinitely many solutions.

An equation like

2x + 3 = -x + 6

Has one solution: x=1

An equation like:

4x + 2 = 4x + 1

Has no solutions because when trying to solve for x we get:

2 = 1

This equality is false and no value of x can make it true

Finally, the equation:

3x + 2 = x + 2x + 2

Has infiniteyl many solutions, because when trying to solve it, we get:

2 = 2

Which is true regardless of the value of x

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

For this equation not having solutions, we should have 8x plus any number but 9 on the right side of the equation:

8x + 9 = 8x -3, or

8x + 9 = 8x + 4

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

If the equation has one solution, the only condition is that we should not have 8x on the right side. Thus any of those will do:

8x + 9 = 3x + 9

8x + 9 = -x + 5

8x + 9 = 0

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

For this equation to have infinitely many solutions, the right side must be exactly equal to the left side:

8x + 9 = 8x + 9