Question

Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6 (1 point)

The equation has no solution.

The equation has one solution: x=6.

The equation has infinite solutions.

The equation has one solution: x=10

Answer 1

To solve the equation \( 5(2x+2)−7x=3x+6 \), we first simplify both sides.

1. Distribute \( 5 \) on the left side:
\[
5 \cdot 2x + 5 \cdot 2 - 7x = 10x + 10 - 7x
\]
This simplifies to:
\[
10x + 10 - 7x = 3x + 10
\]
Combining like terms on the left side:
\[
(10x - 7x) + 10 = 3x + 10
\]
Thus,
\[
3x + 10 = 3x + 6
\]

2. Now, we can subtract \( 3x \) from both sides:
\[
10 = 6
\]

This statement \( 10 = 6 \) is false and indicates that there are no values of \( x \) that satisfy the original equation.

Thus, the conclusion is that **The equation has no solution.**