Question

Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−4=2x+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=1 . The equation has one solution: x equals 1 . The equation has one solution: x=0 .

Answer 1

To solve the equation \(5(2x + 2) - 4 = 2x + 6\), we'll first distribute and simplify both sides.

Start with the left side:

\[
5(2x + 2) - 4 = 10x + 10 - 4 = 10x + 6
\]

Now rewrite the equation:

\[
10x + 6 = 2x + 6
\]

Next, isolate the variable \(x\) by subtracting \(2x\) from both sides:

\[
10x - 2x + 6 = 6
\]

This simplifies to:

\[
8x + 6 = 6
\]

Now, subtract \(6\) from both sides:

\[
8x = 0
\]

Finally, divide both sides by \(8\):

\[
x = 0
\]

Now let's determine the number of solutions. Since we found a specific value for \(x\), the equation has **one solution: \(x = 0\)**.

Thus, the correct response is:
**The equation has one solution: x=0.**