Question

Which of the following equations have infinitely many solutions? Choose all answers that apply: Choose all answers that apply: (Choice A) A x-37=x-37x−37=x−37x, minus, 37, equals, x, minus, 37 (Choice B) B 73x-37=73x-3773x−37=73x−3773, x, minus, 37, equals, 73, x, minus, 37 (Choice C) C 37x-37=37x-3737x−37=37x−3737, x, minus, 37, equals, 37, x, minus, 37 (Choice D) D 74x-37=74x-3774x−37=74x−37

Answer 1

All four equations have infinitely many solutions.

The equation will have infinitely many solutions if both sides of the equation are equal to each other for all values of x. We can check this by combining the terms on one side of the equation and seeing if the other side is equal to zero.

Equation A: x-37=x-37x−37=x−37x, minus, 37, equals, x, minus, 37

Combining the terms on the left side of the equation, we get 0=0. This is true for all values of x, so equation A has infinitely many solutions.

Equation B: 73x-37=73x-3773x−37=73x−3773, x, minus, 37, equals, 73, x, minus, 37

Combining the terms on the left side of the equation, we get 0=0. This is true for all values of x, so equation B has infinitely many solutions.

Equation C: 37x-37=37x-3737x−37=37x−3737, x, minus, 37, equals, 37, x, minus, 37

Combining the terms on the left side of the equation, we get 0=0. This is true for all values of x, so equation C has infinitely many solutions.

Equation D: 74x-37=74x-3774x−37=74x−3774, x, minus, 37, equals, 74, x, minus, 37

Combining the terms on the left side of the equation, we get 0=0. This is true for all values of x, so equation D has infinitely many solutions.

Answer 2

All options are correct.

Explanation:

In option (A), the given equation is

`x-37=x-37`

Add 37 on both sides.

`x-37+37=x-37+37`

`x=x`

Subtract x from both sides.

`x-x=x-x`

`0=0`

LHS=RHS for all values of x. It means equation x-37=x-37 has infinite many solutions.

Similarly.

In option (B), the given equation is

`73x-37=73x-37`

`73x=73x`

`0=0`

LHS=RHS for all values of x. It means equation 73x-37=73x-37 has infinite many solutions.

In option (C), the given equation is

`37x-37=37x-37`

`37x=37x`

`0=0`

LHS=RHS for all values of x. It means equation 37x-37=37x-37 has infinite many solutions.

In option (D), the given equation is

`74x-37=74x-37`

`74x=74x`

`0=0`

LHS=RHS for all values of x. It means equation 74x-37=74x-37 has infinite many solutions.

Therefore, all options are correct.