Question

Select the equation that has infinitely many solutions.(1 point)
Responses

A.3x+5=3x−5


B.3−3x=−3(x−1)

C.3x=2x+1


D.4x+1=4(x+1)

Answer 1

To determine which equation has infinitely many solutions, we can simplify each equation and see if they result in a true statement for all values of \( x \).

**A.** \( 3x + 5 = 3x - 5 \)

Subtract \( 3x \) from both sides:

\( 5 = -5 \) (False statement)

**B.** \( 3 - 3x = -3(x - 1) \)

Simplifying the right side:

\( 3 - 3x = -3x + 3 \)

Now, both sides can be simplified further:

\( 3 - 3x = 3 - 3x \) (True statement for all \( x \))

**C.** \( 3x = 2x + 1 \)

Subtract \( 2x \) from both sides:

\( x = 1 \) (Single solution)

**D.** \( 4x + 1 = 4(x + 1) \)

Distributing on the right side:

\( 4x + 1 = 4x + 4 \)

Subtract \( 4x \) from both sides:

\( 1 = 4 \) (False statement)

Based on the evaluations, the correct answer is:

**B. \( 3 - 3x = -3(x - 1) \) has infinitely many solutions.**