Question

Sole for x to determine if the equation as none, one, or infinite solutions.

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

Answer 1

are you sure

Answer 2

To determine the number of solutions for the equation \( 5(2x + 2) - 4 = 2x + 6 \), we will first simplify the equation.

Starting with the left side:

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

Distributing the 5:

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

Now, we rewrite the equation:

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

Next, we will isolate \( x \) by moving \( 2x \) to the left side:

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

This simplifies to:

\[
8x + 6 = 6
\]

Now, subtract 6 from both sides:

\[
8x = 0
\]

Dividing both sides by 8 gives:

\[
x = 0
\]

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

Answer 3

Let’s double-check the steps to ensure that we correctly solved the equation \(5(2x + 2) - 4 = 2x + 6\).

1. **Start with the given equation:**
\[
5(2x + 2) - 4 = 2x + 6
\]

2. **Distribute on the left side:**
\[
5(2x) + 5(2) - 4 = 2x + 6
\]
This simplifies to:
\[
10x + 10 - 4 = 2x + 6
\]

3. **Combine like terms on the left side:**
\[
10x + 6 = 2x + 6
\]

4. **Now, isolate \(x\) by subtracting \(2x\) from both sides:**
\[
10x - 2x + 6 = 6
\]
Which simplifies to:
\[
8x + 6 = 6
\]

5. **Next, subtract 6 from both sides:**
\[
8x = 0
\]

6. **Finally, divide by 8:**
\[
x = 0
\]

So, the solution \(x = 0\) is indeed correct.

To summarize:
- The left-hand side \(10x + 6\) and the right-hand side \(2x + 6\) become equal when \(x = 0\).
- Since we arrived at a single unique solution, thus the equation has **one solution**: \(x = 0\).

Thank you for your patience, and the result is confirmed to be accurate.