Final answer:
To write an equation with no solution, none of the provided options satisfy the requirement. To write an equation with infinitely many solutions, option c) 2x + 5 = 2x + 5; 3x - 4 = 3x - 4 is the correct choice.
Step-by-step explanation:
To write an equation with no solution, we need to create an equation that leads to a contradiction. Let's examine the options:
- Option a) 2x + 3 = 2x + 5; 2x - 3 = 2x + 3
- Option b) 3x + 4 = 3x + 4; 2x - 3 = 2x + 3
- Option c) 2x + 5 = 2x + 5; 3x - 4 = 3x - 4
- Option d) 4x - 6 = 4x + 2; 3x - 5 = 3x + 1
None of these options have two terms on both sides that cancel out, resulting in a contradiction. Therefore, none of these options have no solution.
To write an equation with infinitely many solutions, we need to create an equation where both sides are always equal, regardless of the value of x. Let's examine the options:
- Option a) 2x + 3 = 2x + 5; 2x - 3 = 2x + 3
- Option b) 3x + 4 = 3x + 4; 2x - 3 = 2x + 3
- Option c) 2x + 5 = 2x + 5; 3x - 4 = 3x - 4
- Option d) 4x - 6 = 4x + 2; 3x - 5 = 3x + 1
Option c) 2x + 5 = 2x + 5; 3x - 4 = 3x - 4 is the only option that always holds true. No matter what value of x we choose, both sides of the equation are always equal.