Use the drop-down menus to complete each equation so the statement about its solution is true. No Solutions 2x + 9 + 3x + x = ___ + ___ One Solution 2x + 9 + 3x + x = ___ + ___ Infinitely Many Solutions 2x + 9 + 3x + x = ___ + ___.

Let’s complete each equation step-by-step:

1. No Solutions: For an equation to have no solutions, the left-hand side must equal a contradictory statement on the right. For example:

[

2x + 9 + 3x + x = 6x + 9 = 6x + 10

]

Here, we have (6x + 9) (left) equal to (6x + 10) (right). This simplifies to (9 = 10), which is false.

2. One Solution: For an equation to have one unique solution, we can set the left-hand side equal to the right-hand side with different coefficients. For example:

[

2x + 9 + 3x + x = 6x + 9 = 2x + 10

]

This balances the left side to a unique value determined by (x) after simplification.

3. Infinitely Many Solutions: To achieve infinitely many solutions, both sides must be equivalent when simplified. For example:

[

2x + 9 + 3x + x = 6x + 9 = 6x + 9

]

In this case, both sides are always equal, allowing for infinitely many values of (x).

So the completed equations look like this:

– No Solutions: (