Recall that for a linear equation to have infinitely many solutions, we have to arrive at a statement that is always true independently of the value of the variable. For that to happen, we have to eliminate the dependence on the variable, therefore, the coefficient of x must be +4.
Now we have half of the problem solved:
![6-3+4x+1=4x+\ldots_{}](https://img.qammunity.org/2023/formulas/mathematics/college/771zuqkf0ymk6th19my2g037z53ofuxstr.png)
To find the other part of the solution, we have to make sure that the equality is true, therefore on both sides, we have to have the same constant, in this case, if we add like terms on the left side we get:
![4x+4.](https://img.qammunity.org/2023/formulas/mathematics/college/t0nj6d2ygnd0irgplovikp3t19atw3k1xu.png)
Therefore, the other missing part of the equation is 4.
Answer:
![6-3+4x+1=4x+4.](https://img.qammunity.org/2023/formulas/mathematics/college/53a5axmgaf9etq4jic7kyqqio85vmn1ghu.png)
Sotty