Equations With Variables On Both Sides?

Explanation
By solving the equation 9x - 12 = 3x, we can find the value of x. First, we can simplify the equation by subtracting 3x from both sides, which gives us 6x - 12 = 0. Then, we can add 12 to both sides to isolate the variable, resulting in 6x = 12. Finally, we divide both sides by 6 to solve for x, getting x = 2. Therefore, the correct answer is 2.

Explanation
In the given equation, we have 8x - 12 on the left side and 15x - 4x on the right side. To solve the equation, we need to simplify both sides by combining like terms. On the left side, we have 8x - 12, and on the right side, we have 15x - 4x which simplifies to 11x. Therefore, the equation becomes 8x - 12 = 11x. To isolate x, we subtract 11x from both sides, resulting in -3x - 12 = 0. Finally, we add 12 to both sides, giving us -3x = 12. Dividing both sides by -3, we find that x = -4.

Explanation
To find the value of x in the equation 11 + 6x = 2x - 13, we need to isolate the variable x. First, we can simplify the equation by combining like terms. By subtracting 2x from both sides, we get 9 + 4x = -13. Next, by subtracting 9 from both sides, we obtain 4x = -22. To solve for x, we divide both sides by 4, which gives us x = -5.5. However, since the given answer choices are integers, we round down to the nearest whole number, resulting in x = -6.

Explanation
The given equation is -5x = 9 - 2x. To solve for x, we can combine like terms by adding 2x to both sides of the equation, which gives -3x = 9. Then, we divide both sides of the equation by -3 to isolate x, resulting in x = -3. Therefore, the correct answer is -3.

Explanation
To solve the equation -8x - 10 = 4x + 14, we need to isolate the variable x. First, we can add 8x to both sides of the equation to eliminate the variable on the left side. This gives us -10 = 12x + 14. Next, we can subtract 14 from both sides to move the constant term to the right side. This gives us -24 = 12x. Finally, we can divide both sides by 12 to solve for x. This gives us x = -2. Therefore, the correct answer is -2.

Explanation
The given equation is a linear equation in one variable. To solve it, we can start by simplifying both sides of the equation. By adding 3x to both sides and adding 5 to both sides, we get 13x = 26. Dividing both sides by 13, we find that x = 2. Therefore, the equation is satisfied when x = 2.

Explanation
To solve the equation -12x = 14 - 5x, we need to isolate the variable x. We can do this by combining like terms. Subtracting -5x from both sides of the equation, we get -12x + 5x = 14. Simplifying this, we have -7x = 14. To solve for x, we divide both sides of the equation by -7. This gives us x = -2. Therefore, the correct answer is -2.

Explanation
In the given equation, 4x + 12 = -3x - 6 + 4x, we need to simplify and solve for x. By combining like terms, we can simplify the equation to 8x + 12 = -6. Next, by subtracting 12 from both sides, we get 8x = -18. Finally, dividing both sides by 8, we find that x = -2.25. Therefore, the answer -6 is incorrect and does not correspond to any step in the solution process.