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 one solution: x=6. The equation has one solution: x equals 6 . The equation has infinite solutions. The equation has infinite solutions. The equation has one solution: x=10.

Answer 1

Let's solve the equation \(5(2x + 2) - 7x = 3x + 6\).

First, distribute \(5\) on the left side:

\[
5 \cdot 2x + 5 \cdot 2 - 7x = 3x + 6
\]

This simplifies to:

\[
10x + 10 - 7x = 3x + 6
\]

Now, combine like terms on the left side:

\[
(10x - 7x) + 10 = 3x + 6
\]

This results in:

\[
3x + 10 = 3x + 6
\]

Next, we can subtract \(3x\) from both sides:

\[
10 = 6
\]

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

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