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 one solution: x=10. The equation has one solution: x equals 10 . The equation has one solution: x=6. The equation has one solution: x equals 6 . The equation has no solution. The equation has no solution. The equation has infinite solutions.

Answer 1

are you sure

Answer 2

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

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

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

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

Now, combine like terms on the left side:

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

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

Next, isolate the variable \( x \) by subtracting \( 3x \) from both sides:

\[
10 = 6
\]

This statement \( 10 = 6 \) is always false, which indicates that there are no solutions for this equation.

Therefore, the equation has no solution.

Answer 3

Yes, I’m confident in the solution. Let’s step through the equation again for clarity.

The original equation is:

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

1. Distribute the \(5\):

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

2. Combine like terms on the left:

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

This simplifies to:

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

3. Now, subtract \(3x\) from both sides:

\[
10 = 6
\]

This is a contradiction because \(10\) does not equal \(6\).

Since we reached an impossible statement, it confirms that the original equation has **no solutions**.

So, the correct conclusion is that the equation has no solution. If you have further doubts or questions, please let me know!