No Solutions 6−3+4x+1= x + One Solution 6−3+4x+1= x + Infinitely Many Solutions 6−3+4x+1= x +

Complete Question:

Complete each equation, so the statement about its solution is true.

No solutions:

6-3+4x+1= __x + __

One solution:

6-3+4x+1= __x + __

Infinitely many solutions:

6-3+4x+1 = __x + __

--- No solution

--- One solution

--- Infinitely Many solution

Step-by-step explanation:

Solving (a): No solutions

6-3+4x+1= __x + __

Collect like terms

6-3+1+4x= __x + __

4+4x= __x + __

To get no solution, the coefficient of x on both sides must be the same. However, the constant must be different.

So, we can equate the expression to:

Solving (b): One solution

6-3+4x+1= __x + __

This gives (same as (a))

4+4x= __x + __

To get one solution, the coefficient of x on both sides must be different. The constant can have any value.

So, we can equate the expression to:

Solving (c): Infinitely many solutions

6-3+4x+1= __x + __

This gives (same as (a))

4+4x= __x + __

To get infinitely many solutions, both sides of the equation must be equal.

So:

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step-by-step explanation: