Question

Solve for x to determine if the equation has one, none, or infinite solutions. 3(2x+2)−4=−2x+10 (1 point) Responses The equation has one solution: x=1 . The equation has one solution: x equals 1 . The equation has no solution. The equation has no solution. The equation has one solution: x=0 . The equation has one solution: x equals 0 . The equation has infinite solutions.

Answer 1

Let's solve the equation step by step to determine the number of solutions.

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

First, distribute the \( 3 \):
\[ 6x + 6 - 4 = -2x + 10 \]

Now, simplify the left side:
\[ 6x + 2 = -2x + 10 \]

Next, add \( 2x \) to both sides:
\[ 6x + 2x + 2 = 10 \]
\[ 8x + 2 = 10 \]

Now, subtract \( 2 \) from both sides:
\[ 8x = 8 \]

Then, divide both sides by \( 8 \):
\[ x = 1 \]

Now that we have found \( x = 1 \), we can conclude that the equation has one solution.

The correct response is:
The equation has one solution: x=1.