To answer these problems, it would be best to think about each one conceptually. To get an answer with no solutions, the graphs of the equations on either side of the equal sign would have to be parallel - in being so, they never <em>equal</em> each other and have no solutions. Similarly, having one solution would require the graphs to intersect at only one point, and to have infinitely many solutions, they’d have to be the same graph on either side of the equal sign.
For no solutions, you’d need the slope to match and have a different <em>+b</em> value. You’ve done this correctly; 3x + 1 is parallel to 3x and you’ll have no solutions.
For one solution, you simply need a different slope. The slope on the left will be 3 forever, so you can choose any other value for _x on the right; 6, 12, 375, eight million, or even 0 would satisfy this problem.
For infinitely many solutions, the two sides must equal exactly. In this case, the right side must be 3x + 1 to match the left’s 3x + 1, which you have also done correctly. Congratulations!
Hope this helps!
