Question

Solve for x
to determine if the equation has one, none, or infinite solutions.
3(2x+2)−10x=−4x+6
(1 point)
Responses

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=−1
.
The equation has one solution: x equals negative 1 .

The equation has no solution.

Answer 1

Let's solve the equation step by step:

Given:
\[ 3(2x + 2) - 10x = -4x + 6 \]

First, distribute the 3 on the left side:
\[ 6x + 6 - 10x = -4x + 6 \]

Now, combine like terms on the left side:
\[ (6x - 10x) + 6 = -4x + 6 \]
\[ -4x + 6 = -4x + 6 \]

Now, we can see that both sides of the equation are equal. This indicates that the equation is true for all values of \( x \).

Thus, the equation has infinite solutions.

**Final answer:** The equation has infinite solutions.