Question

Which equation has infinitely many solutions? Responses 3(x+1)=3x+3 3 ( x + 1 ) = 3 x + 3 3(x+1)=3 3 ( x + 1 ) = 3 3(x+1)=3x+1 3 ( x + 1 ) = 3 x + 1 3(x+1)=1

Answer 1

The equation among the given options that has infinitely many solutions is 3(x + 1) = 3x + 3, because after simplifying it, you end up with a statement that is always true, which is 3 = 3.

Step-by-step explanation:

The question asks which equation has infinitely many solutions. An equation has infinitely many solutions if, after simplifying, you end up with a statement that is always true, such as 0 = 0.

Let's examine the provided equations:

1. 3(x + 1) = 3x + 3: Upon distribution, we get 3x + 3 = 3x + 3. Subtracting 3x from both sides gives us 3 = 3, which is always true, so this equation has infinitely many solutions.
2. 3(x + 1) = 3: Distributing and simplifying gives us 3x + 3 = 3, which upon subtracting 3 from both sides yields 3x = 0, or x = 0. This equation has a single solution.
3. 3(x + 1) = 3x + 1: After distribution, we have 3x + 3 = 3x + 1. Subtracting 3x from both sides, we get 3 = 1, which is never true. This equation has no solutions.
4. 3(x + 1) = 1: Distributing results in 3x + 3 = 1. Subtracting 3 from both sides leads to 3x = -2, or x = -2/3, so this equation also has a single solution.

The equation with infinitely many solutions is the first one: 3(x + 1) = 3x + 3.