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=10
.
The equation has one solution: x equals 10 .

The equation has one solution: x=6
.

Answer 1

To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), let's first simplify both sides.

**Step 1: Distribute on the left side**

\[
5(2x + 2) = 10x + 10
\]

So our equation becomes:

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

**Step 2: Combine like terms on the left side**

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

**Step 3: Subtract \(3x\) from both sides**

\[
10 = 6
\]

This statement is not true. Since we have reached a contradiction, it means that there is **no solution** to the equation.

Thus, the answer is:

**The equation has no solution.**