solve the solution

To solve the equation \( 2x + 3 = 2x + 7 \), we can start by attempting to isolate \( x \).

1. Subtract \( 2x \) from both sides: \[ 2x + 3 - 2x = 2x + 7 - 2x \] which simplifies to: \[ 3 = 7 \]

This statement \( 3 = 7 \) is false.

Since we arrived at a contradiction, this means that the original equation has no solutions. Thus, the equation is inconsistent.

To solve the equation \( 7x + 3 = 7x + 3 \), we follow similar steps to isolate \( x \).

1. Subtract \( 7x \) from both sides: \[ 7x + 3 - 7x = 7x + 3 - 7x \] which simplifies to: \[ 3 = 3 \]

This statement \( 3 = 3 \) is always true.

Since the equation holds true for any value of \( x \), it indicates that there are infinitely many solutions for this equation. In this case, any value of \( x \) will satisfy the equation.

To solve the equation \( 4x + 22 = 8x + 10 \), we can isolate \( x \) by following these steps:

1. Subtract \( 4x \) from both sides: \[ 4x + 22 - 4x = 8x + 10 - 4x \] which simplifies to: \[ 22 = 4x + 10 \]

2. Next, subtract \( 10 \) from both sides: \[ 22 - 10 = 4x + 10 - 10 \] which simplifies to: \[ 12 = 4x \]

3. Now, divide both sides by \( 4 \): \[ \frac{12}{4} = x \] which simplifies to: \[ x = 3 \]

So, the solution to the equation \( 4x + 22 = 8x + 10 \) is \( x = 3 \).

Since we found a specific value for \( x \), this equation has one solution.

To solve the equation \( 5x + 5 = 5x + 4 \), we can isolate \( x \) by following these steps:

1. Subtract \( 5x \) from both sides: \[ 5x + 5 - 5x = 5x + 4 - 5x \] This simplifies to: \[ 5 = 4 \]

The statement \( 5 = 4 \) is false, which indicates that the original equation has no solutions.

Thus, the equation \( 5x + 5 = 5x + 4 \) is inconsistent, and it has no solutions.