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=

For no solution,

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

For one solution,

2x + 9 + 3x + x = 15

For infinitely many solutions,

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

Step-by-step explanation:

1. 2x + 9 + 3x + x = 6x

6x + 9 = 6x

Subtract 6x from both sides,

9 = 0 which is absurd and hence the equation has no solution.

2. 2x + 9 + 3x + x = 15

6x + 9 = 15

Subtract 9 from both sides.

6x = 6

Divide both sides by 6.

x = 1 and this is the only solution.

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

6x + 9 = 6x + 9

Subtract 6x from both sides,

9 = 9, both sides are balanced which means, the equation has infinitely many solutions.

no solution : 6x + 7

one solution : 2x + 0

Infinitely possible solution : 6x + 9