Question

Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6(1 point) Responses The equation has no solution. The equation has no solution. The equation has infinite solutions. The equation has infinite solutions. The equation has one solution: x=6. The equation has one solution: x equals 6 . The equation has one solution: x=10. The equation has one solution: x equals 10 .

Answer 1

To solve the equation \( 5(2x+2) - 7x = 3x + 6 \), we can follow these steps:

1. **Distribute** the \( 5 \):
\[
5(2x) + 5(2) - 7x = 3x + 6
\]
This simplifies to:
\[
10x + 10 - 7x = 3x + 6
\]

2. **Combine like terms** on the left side:
\[
(10x - 7x) + 10 = 3x + 6
\]
This simplifies to:
\[
3x + 10 = 3x + 6
\]

3. **Subtract \( 3x \) from both sides**:
\[
10 = 6
\]

Since \( 10 \neq 6 \), this is a contradiction. Thus, the original equation has no solution.

Final answer: **The equation has no solution.**