To solve the equation \(7x + 5x + 6 = -2 + 2(5x + 10)\), we can start by simplifying both sides. 1. Combine like terms on the left side: \[ 7x + 5x + 6 = 12x + 6 \] 2. Simplify the right side: \[ -2 + 2(5x + 10) = -2 + 10x + 20 = 10x + 18 \] Now the equation looks like this: \[ 12x + 6 = 10x + 18 \] 3. Next, isolate \(x\) by subtracting \(10x\) from both sides: \[ 12x - 10x + 6 = 18 \] This simplifies to: \[ 2x + 6 = 18 \] 4. Now, subtract \(6\) from both sides: \[ 2x = 18 - 6 \] This gives us: \[ 2x = 12 \] 5. Finally, divide both sides by \(2\): \[ x = 6 \] So the solution to the equation \(7x + 5x + 6 = -2 + 2(5x + 10)\) is: \[ \boxed{6} \]

4x + 12 = 4x + 8

To solve the equation \(4x + 12 = 4x + 8\), we can start by simplifying both sides.

Subtract \(4x\) from both sides:

\[ 4x + 12 - 4x = 4x + 8 - 4x \]

This simplifies to:

\[ 12 = 8 \]

Since \(12\) does not equal \(8\), this means that the original equation has no solutions.

Thus, the equation \(4x + 12 = 4x + 8\) is a contradiction, indicating that there is no value of \(x\) that can satisfy it.

7x + 5x + 6 = -2 + 2 (5x + 10)

To solve the equation \(7x + 5x + 6 = -2 + 2(5x + 10)\), we can start by simplifying both sides.

Combine like terms on the left side:

\[ 7x + 5x + 6 = 12x + 6 \]

Simplify the right side:

\[ -2 + 2(5x + 10) = -2 + 10x + 20 = 10x + 18 \]

Now the equation looks like this:

\[ 12x + 6 = 10x + 18 \]

Next, isolate \(x\) by subtracting \(10x\) from both sides:

\[ 12x - 10x + 6 = 18 \]

This simplifies to:

\[ 2x + 6 = 18 \]

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

\[ 2x = 18 - 6 \]

This gives us:

\[ 2x = 12 \]

Finally, divide both sides by \(2\):

\[ x = 6 \]

So the solution to the equation \(7x + 5x + 6 = -2 + 2(5x + 10)\) is:

\[ \boxed{6} \]