Question

Solve for x to determine if the equation has one, none or infinite solutions.

5 (2x + 2) - 4 = 2x + 6

answers:

The equation has one solution: x = 0

The equation has no solutions

The equation has infinite solutions.

The equation has one solution: x = 1

Answer 1

are you sure

Answer 2

Let's solve the equation step by step:

The given equation is:

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

1. Distribute the 5 on the left side:

\[ 10x + 10 - 4 = 2x + 6 \]
\[ 10x + 6 = 2x + 6 \]

2. Now, subtract \(2x\) from both sides:

\[ 10x - 2x + 6 = 6 \]
\[ 8x + 6 = 6 \]

3. Next, subtract 6 from both sides:

\[ 8x = 0 \]

4. Finally, divide by 8:

\[ x = 0 \]

Now, let's determine the type of solution:

Since we found one specific solution \(x = 0\), the equation has **one solution**.

Thus, the answer is:

**The equation has one solution: x = 0**.

Answer 3

Let's go through the problem again step by step to ensure the solution is correct.

Starting with the original equation:

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

1. Distribute the \(5\) on the left side:

\[
5 \cdot 2x + 5 \cdot 2 - 4 = 2x + 6
\]
This simplifies to:
\[
10x + 10 - 4 = 2x + 6
\]
So now we have:
\[
10x + 6 = 2x + 6
\]

2. Next, subtract \(2x\) from both sides:

\[
10x - 2x + 6 = 6
\]
This simplifies to:
\[
8x + 6 = 6
\]

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

\[
8x + 6 - 6 = 6 - 6
\]
This gives us:
\[
8x = 0
\]

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

\[
x = 0
\]

Now, let's determine if the equation has one solution, no solutions, or infinite solutions:

Since we obtained a specific solution of \(x = 0\), the equation indeed has **one solution**.

Therefore, the conclusion is correct:

**The equation has one solution: x = 0**.