Question

Which of the following equations have infinitely many solutions?

1) [74x-37=74x-37]
2) [73x-37=73x-37]
3) [x-37=x-37]
4) [37x-37=37x-37]

Answer 1

All the provided equations, [74x-37=74x-37], [73x-37=73x-37], [x-37=x-37], and [37x-37=37x-37], have infinitely many solutions because upon simplification each equation reduces to a true statement regardless of the value of x.

Step-by-step explanation:

The question asks which of the following equations have infinitely many solutions: 1) [74x-37=74x-37] 2) [73x-37=73x-37] 3) [x-37=x-37] 4) [37x-37=37x-37]. An equation has infinitely many solutions when both sides are the same for all values of the variable.

• For equation (1) [74x-37=74x-37], if we subtract 74x from both sides, we get -37 = -37, which is always true regardless of the value of x. Therefore, this equation has infinitely many solutions.
• The same logic applies to equations (2), (3), and (4). After simplification, each of these equations reduces to a statement that is always true (e.g., 0 = 0), indicating that they also have infinitely many solutions.

Thus, all the given equations (1, 2, 3, and 4) have infinitely many solutions.